Solved: "Find the derivatives of the following function.y=(2x3+7)(3x3+5)y'=" - Plainmath

Reggie

Answered question

2021-10-23

Find the derivatives of the following function.

y = (2 x^{3} + 7) (3 x^{3} + 5)

y'=

Answer & Explanation

SchepperJ

Skilled2021-10-24Added 96 answers

Step 1:- Introduction:-
Given function

y = (2 x^{3} + 7) (3 x^{3} + 5)

Step 2:- Calculation:-

y = (2 x^{3} + 7) (3 x^{3} + 5)

Differentiating w.r.t 'x' we get

\frac{d y}{d x} = (2 x^{3} + 7) \frac{d}{d x} (3 x^{3} + 5) + (3 x^{3} + 5) \frac{d}{d x} (2 x^{3} + 7)

\frac{d y}{d x} = (2 x^{3} + 7) (9 x^{2}) + (3 x^{3} + 5) (6 x^{2})

\frac{d y}{d x} = 18 x^{5} + 63 x^{2} + 18 x^{5} + 30 x^{2}

\frac{d y}{d x} = 36 x^{5} + 93 x^{2}

Step 3:- Conclusion:-
The answer is

y^{'} = 36 x^{5} + 93 x^{2}

Jeffrey Jordon

Expert2022-03-13Added 2605 answers

Answer is given below (on video)

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