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Differentiate (a) with respect to x ( y is a function of x) and (b) with respect to t (x and y are functions of t).

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Differentiate (a) with respect to x ( y is a function of x) and (b) with respect to t (x and y are functions of t).

cos πy - 3 sin πx = 1
asked Jan 22, 2015 in CALCULUS by anonymous

1 Answer

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Step 1 :

(a)

y  is a functions of x, that means image.

The function is image.

Differentiate implicitly with respect to x.

image

Apply chain rule : image.

image

The derivative of the function with respect to x :

image

Step 2 :

(b)

x,y are functions of t, that means image and image.

The function is image.

Differentiate implicitly with respect to t.

image

Apply chain rule.

image

The derivative of the function with respect to x:

image

Solution :

(a) image

(b) image

answered Jan 22, 2015 by Thomas Apprentice

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