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Elleanor Mckenzie

Answered question

2021-04-30

Derivatives of the sum of functions Find the derivative of the following functions.

f (x) = 3 x^{4} + 7 x

timbalemX

Skilled2021-05-02Added 108 answers

Step 1
We have to find the derivatives of following function:
We know the formula of derivatives,

\frac{{d x}^{n}}{d x} = n x^{n - 1}

(power rule)

\frac{d a x^{n}}{d x} = a \frac{{d x}^{n}}{d x}

(where a is some constant)

\frac{d x}{d x} = 1

\frac{d (c o n s \tan t)}{d x} = 0

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

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

Applying above formulae for the given functions:
Differentiating the given function with respect to 'x', we get

\frac{d f (x)}{d x} = \frac{d (3 x^{4} + 7 x)}{d x}

f^{'} (x) = 3 \frac{{d x}^{4}}{d x} + 7 \frac{d x}{d x}

= 3 (4 x^{4 - 1}) + 7 \times 1

= 12 x^{3} + 7

Hence, derivative of the function is

12 x^{3} + 7

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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