Find out the answer to "Find the derivatives of the following function.f(x)=7x5+3x3−ex3f′(x)=" - Plainmath

Amari Flowers

Answered question

2021-10-20

Find the derivatives of the following function.
$f (x) = 7 x^{5} + 3 x^{3} - e x^{3}$
$f^{'} (x) =$

Answer & Explanation

Bentley Leach

Skilled2021-10-21Added 109 answers

Step 1
Given:

f (x) = 7 x^{5} + 3 x^{3} - e x^{3}

To find f'(x)
Step 2

f (x = 7 x^{5}) + 3 x^{3} - e x^{3}

f^{'} (x) = \frac{d}{d x} (f (x))

= \frac{d}{d x} (7 x^{5} + 3 x^{3} - e x^{3})

Apply sum rule:

{(f \pm g)}^{'} = f^{'} \pm g^{'}

\frac{d}{d x} (7 x^{5} + 3 x^{3} - e x^{3}) = \frac{d}{d x} 7 x^{5} + \frac{d}{d x} 3 x^{3} \frac{d}{d x} - e x^{3}

= 7 \cdot 5 x^{4} + 3 \cdot 3 x^{2} - e \cdot 3 x^{2}

= 35 x^{4} + 9 x^{2} - 3 e x^{2}

f^{'} (x) = 35 x^{4} + 9 x^{2} - 3 e x^{2}

Jeffrey Jordon

Expert2022-03-13Added 2605 answers

Answer is given below (on video)

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