Find f'(x). f(x)=(9x^2 8)^6(4x^2 5)^{11}

Question:

Find {eq}f'(x) {/eq}. {eq}f(x)=(9x^2 8)^6(4x^2 5)^{11} {/eq}

Differentiation:

In this question simple differentiation is given as more complex form.

The only way to solve this is go step by step.

In every step we need to avoid error and also consider chain rule function.

Answer and Explanation:

We have,

{eq}f(x)=(9x^2 8)^6(4x^2 5)^{11} {/eq}

now,

On differentiating,

{eq}f'(x)=((9x^2 8)^6)'(4x^2 5)^{11} + (9x^2 8)^6((4x^2 5)^{11})' \\ f'(x)=6(9x^2 8)^5(144x)(4x^2 5)^{11} + (9x^2 8)^6 11(4x^2 5)^{10}(40x) \\ f'(x)=864x(72x^2 )^5(20x^2 )^{11} + 440x(72x^2 )^6(20x^2 )^{10} \\ {/eq}

so,

{eq}\therefore \color{blue}{\displaystyle f'(x)=864x(72x^2 )^5(20x^2 )^{11} + 440x(72x^2 )^6(20x^2 )^{10} } {/eq}


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Basic Calculus: Rules & Formulas

from Calculus: Tutoring Solution

Chapter 3 / Lesson 6
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