Chapter 9.8, Problem 14E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# In Problems 13-24, find the indicated derivative. 14.  If  y = x 4 + x 1 / 3 ,  find d 2 y d x 2 .

To determine

To calculate: The second derivative of the function y=x4+x13.

Explanation

Given Information:

The function is y=x4+x13.

Formula used:

According to the power rule, if f(x)=xn, then,

fâ€²(x)=nxnâˆ’1

According to the property of differentiation, if a function is of the form g(x)=cf(x) then,

gâ€²(x)=cfâ€²(x)

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

fâ€²(x)=uâ€²(x)+vâ€²(x)

Calculation:

Consider the provided function,

y=x4+x13

To find the first order derivative, differentiate both sides with respect to x,

dydx=ddx(x4+x13)=ddx(x4)+ddx(x13)

Apply the power rule and rule of differentiating a constant,

dydx=(4â‹…x4âˆ’1)+(13â‹…x13âˆ’1)=4x

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