Step by step solution to "Find the derivative g(x)=πx3−cos⁡x+20"

sanuluy

Answered question

2021-10-20

Find the derivative

g (x) = π x^{3} - \cos x + \sqrt{20}

Answer & Explanation

Malena

Skilled2021-10-21Added 83 answers

Step 1
For a function f the derivative is defined as

f^{'} (x) = lim_{h \to 0} \frac{f (x + h) - f (x)}{h}

. For some standard functions the derivative is known so if the function is in terms of standard functions then the definition need not be used to compute the derivative.
Use one standard derivative

\frac{d}{d x} x^{n} = n x^{n - 1}, n \neq 0

. Use another standard derivative

\frac{d}{d x} \cos x = - \sin x

. The derivative of a constant is equal to 0. Use the property of derivatives:

\frac{d}{d x} (f (x) + g (x)) = \frac{d}{d x} f (x) + \frac{d}{d x} g (x)

.
Step 2
The function given is

g (x) = π x^{3} - \cos x + \sqrt{20}

. Use information from step 1 to compute the derivative of this function.

g (x) = π x^{3} - \cos x + \sqrt{20}

\frac{d g (x)}{d x} = \frac{d}{d x} (π x^{3} - \cos x + \sqrt{20})

= \frac{d}{d x} (π x^{3}) - \frac{d}{d x} \cos x + \frac{d}{d x} \sqrt{20}

= π \cdot 3 x^{2} - (- \sin x) + 0

= 3 π x^{2} + \sin x

Hence, the derivative of the given function is

3 π x^{2} + \sin x

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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