Calculating derivatives Find dy&gt;dx for the following functions. y=5x2+cos⁡x

Explained: "Calculating derivatives Find dy>dx for the following functions...."

FizeauV

2021-10-04

Calculating derivatives Find dy>dx for the following functions.

y = 5 x^{2} + \cos x

liingliing8

Skilled2021-10-05Added 95 answers

Step 1
To find:
The derivative of

y = 5 x^{2} + \cos x

.
Formula used:
Sum rule of derivative:

\frac{d}{d x} (u + v) = \frac{d}{d x} (u) + \frac{d}{d x} (v)

Power rule of derivative:

{(x^{n})}^{'} = n \cdot x^{n - 1}

Trigonometric function derivative:

{(\cos x)}^{'} = - \sin x

Step 2
Calculation:
The derivative of

y = 5 x^{2} + \cos x

can be obtained as,

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

= \frac{d}{d x} (5 x^{2}) + \frac{d}{d x} (\cos x)

= 5 (2 \cdot x^{2 - 1}) - \sin x

= 10 x - \sin x

Thus, the value is

\frac{d y}{d x} = 10 x - \sin x

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

Answer is given below (on video)

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