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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find an equation of the tangent line to the curve at the given point.

y = ex cos x, (0, 1)

To determine

To find: An equation of the tangent line to the curve y at point (0,1).

Explanation

Given:

The function is y=excosx.

Formula used:

Product Rule:

If f(x) and g(x) are both differentiable function, then Product Rule is,

ddx[f(x)g(x)]=f(x)ddx[g(x)]+g(x)ddx[f(x)] (1)

The slope of the tangent line y is dydx=m at x1 (2)

The equation of tangent line is (yy1)=m(xx1) at the point (x1,y1) (3)

Calculation:

Find derivative of the function y=excosx using Product Rule as shown in equation (1).

ddx[excosx]=exddx[cosx]+cosxddx[ex]=ex(

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