Find out the answer to "Derivatives of the sum of functions Find the..."

Dolly Robinson

Answered question

2021-02-27

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

f (x) = 10 x^{4} - 32 x + \frac{1}{2}

mhalmantus

Skilled2021-03-01Added 105 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 (10 x^{4} - 32 x + \frac{1}{2})}{d x}

f^{'} (x) = 10 \frac{{d x}^{4}}{d x} - 32 \frac{d x}{d x} + \frac{d \frac{1}{2}}{d x}

= 10 (4 x^{4 - 1}) - 32 \times 1 + 0

= 40 x^{3} - 32

= 8 (5 x^{3} - 4)

Hence, derivative of the function is

8 (5 x^{3} - 4)

Jeffrey Jordon

Expert2022-01-31Added 2605 answers

Answer is given below (on video)

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