Chapter 9.4, Problem 22E

### 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 19-26, find the derivative of each function. w = 5 u 8 / 5 − 3 u 5 / 6 + u 1 / 3 + 5

To determine

To calculate: The derivative of the function w=5u8/53u5/6+u1/3+5.

Explanation

Given Information:

The provided function is w=5u8/5âˆ’3u5/6+u1/3+5.

Formula Used:

Sum rule for function f(x)=u(x)+v(x), where u and v are differentiable functions of x, then fâ€²(x)=uâ€²(x)+vâ€²(x).

Difference rule for function f(x)=u(x)âˆ’v(x), where u and v are differentiable functions of x, then fâ€²(x)=uâ€²(x)âˆ’vâ€²(x).

Power of x rule for a real number n is such that, if f(x)=xn then fâ€²(x)=nxnâˆ’1.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x).

Constant function rule for a constant c is such that, if f(x)=c then fâ€²(x)=0.

Calculation:

Consider the function, w=5u8/5âˆ’3u5/6+u1/3+5

Differentiate with respect to u,

dwdu=ddu(5u8/5âˆ’3u5/6+u

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