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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

Differentiate the function.

y = x + x x 2

To determine

To find: The derivative of the function y=x+xx2.

Explanation

Given:

The function, y=x+xx2.

Formula used:

The Power Rule:

If n is any real number, then the power rule is,

ddx(xn)=nxn1 (1)

The Sum Rule:

If f(x) and g(x) are both differentiable functions, then the sum rule is,

ddx[f(x)+g(x)]=ddx[f(x)]+ddx[g(x)] (2)

Calculation:

The derivative of y is dydx, which is obtained as follows:

dydx=ddx(y) =ddx(x+xx2)=ddx(x12+xx2)=ddx(x12x2+xx2)              

dydx=ddx((x12×x2)+(x×x2))ddx

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