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{"id":4651,"date":"2021-11-20T13:41:18","date_gmt":"2021-11-20T13:41:18","guid":{"rendered":"https:\/\/dailyonoff.com\/?p=4651"},"modified":"2021-11-20T13:51:08","modified_gmt":"2021-11-20T13:51:08","slug":"how-do-you-find-the-partial-derivative-of-a-function","status":"publish","type":"post","link":"https:\/\/dailyonoff.com\/how-do-you-find-the-partial-derivative-of-a-function\/","title":{"rendered":"How Do You Find the Partial Derivative of a Function?"},"content":{"rendered":"

How Do You Find the Partial Derivative of a Function?<\/p>\n

The partial derivatives are used in vector calculus and differential geometry to find derivatives of a
\nfunction having several, but we find the derivative with respect to one of its variables. By using the partial
\nderivatives we find the differential equation, which is used to find the points of maximum and the
\nminimum points when analyzing a surface, or plotting a graph. We can use the partial derivatives<\/a>
\ncalculator<\/a> to find the partial derivative of the function in a three-dimensional plane.\u00a0 Basically, we do
\nderivation to find the rate of change or a slope of a tangent line. When we are working on the three-
\ndimensional surface, we use the partial derivative to find how the function is changing at any given point;
\nthese surfaces are perpendicular to each other, in a three-dimensional plane.
\nIn this article we try to understand the partial derivative and the simple method of how to solve it:<\/p>\n

How we can define the partial derivative<\/h2>\n

We can understand the partial derivative by its definition, considering a function f(x,y), the function depends
\non two variables x and y, the x and y are independent of each other but have a direct relation with the rate
\nof change of the function f. In this situation, the derivative we get is a partial derivative. When we solve
\nthe derivative with respect to x, then we consider y is a constant if we are calculating the derivative with
\nrespect to y, we then consider x and a constant one. The partial derivative can be calculated by a partial
\nderivative solver, this would also increase your understanding of the partial derivative.<\/p>\n

The partial derivative symbol and formula.<\/h2>\n

When we are calculating the partial derivative with respect to x, then the symbols of the partial derivative
\nwith respect to the x are f\u2019x, \u2202xf or \u2202f\/\u2202x, the symbol of the partial derivative is \u201c\u2202\u201d.
\nNow if f(x,y) is a function, and we want to find the partial derivative with respect to x and keep the \u201cy\u201d as
\na constant, Then the\u00a0 formula would be:
\nfx=fx=limh0f(x+h,y)-f(x,y)h
\nNow the formula for the partial derivative with respect to y, and keeping the x a constant, we get:
\nfy=fy=limh0f(x,y+h)-f(x,y)h
\nWe can find the second derivative by using the partial derivatives calculator, for our convenience.<\/p>\n

Example:<\/h2>\n

Now\u00a0 consider a function f = \u00a0x 3 + 4xy, this function has more than one variable, we can find its derivative
\nby partial derivative method, we can use the partial derivative calculator to find the partial derivative of this
\nfunction:
\nfx=x( x 3 + 4xy)=3×2+4y
\nNow to find the tangent line slope at point P(2,2) and we can put the values to find the slope of the tangent:
\nThe value of the fxat (2,2) is :
\n3×2+4y=3(2)2+ 4(2)=3(4)+8=12+8=20<\/p>\n

This means the slope of the tangent line is 20, therefore the x=20 at (2,2), for finding the partial derivative
\ndirectly, we can use the partial derivative calculator.<\/p>\n

Partial derivative rules:<\/h2>\n

There are four types of rules for partial derivative, product rule, quotient rule, power, and the chain rule for
\npartial derivative:
\nProduct rule:
\nIf\u00a0 we need to multiply two partial derivatives, we apply the following product rule:
\nIf u=f(x,y).g(x,y) , then we multiply as:
\nUx=Ux=g(x,y) fx+f(x,y) gx
\nUy=Uy=g(x,y) fy+f(x,y) gy
\nThe product of derivatives can be found by using the partial derivative calculator, to avoid the length
\nproduct calculations.<\/p>\n

There are separate formulas for quotient, power, and chain rules formulas for the partial derivative; we can
\nuse the derivative chain rule calculator to find the partial derivative of the independent variables.<\/p>\n

 <\/p>\n

INFORMATIVE: How a worthy education franchise can help you open your own pre-school<\/a><\/h4>\n","protected":false},"excerpt":{"rendered":"

How Do You Find the Partial Derivative of a Function? The partial derivatives are used in vector calculus and differential geometry to find derivatives of a function having several, but we find the derivative with respect to one of its variables. By using the partial derivatives we find the differential equation, which is used to …<\/p>\n","protected":false},"author":1,"featured_media":4652,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[90],"tags":[],"class_list":["post-4651","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-education"],"yoast_head":"\nHow Do You Find the Partial Derivative of a Function?<\/title>\n<meta name=\"description\" content=\"How Do You Find the Partial Derivative of a Function? 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