Question

Find the derivative of y = 4x^3.
Find the derivative of y = 2/x^4.
Find the derivative of y = 3√x.
Find the derivative of y = 3/√x.
Find the derivative of y = x^3/4.
Find the derivative of y = 3 x^5.​

Answer 1

Answer:

$\fbox {See below} \downarrow$

Step-by-step explanation:

Question 1 :

$\mathsf {\frac{dy}{dx} = \frac{d}{dx}(4x^{3})}$

$\mathsf {\frac{dy}{dx} = 4(3)x^{3-1}}$

$\mathsf {\frac{dy}{dx} = 12x^{2}}$

Question 2 :

$\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{2}{x^{4}})}$

$\mathsf {\frac{dy}{dx} = \frac{d}{dx}(2x^{-4})}$

$\mathsf {\frac{dy}{dx} = 2(-4)x^{-4-1}}$

$\mathsf {\frac{dy}{dx} = -8x^{-5}}$

$\mathsf {\frac{dy}{dx} = -\frac{8}{x^{5}}}$

Question 3 :

$\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3\sqrt{x})}$

$\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3(x)^{\frac{1}{2}})}$

$\mathsf {\frac{dy}{dx} = 3(\frac{1}{2})x^{\frac{1}{2}-1}}$

$\mathsf {\frac{dy}{dx} = \frac{3}{2}x^{-\frac{1}{2}}}$

$\mathsf {\frac{dy}{dx} = \frac{3}{2\sqrt{x}}}$

Question 4 :

$\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{3}{\sqrt{x}})}$

$\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{-\frac{1}{2}})}$

$\mathsf {\frac{dy}{dx} = 3(-\frac{1}{2})x^{-\frac{1}{2}-1}}$

$\mathsf {\frac{dy}{dx} = -\frac{3}{2}x^{-\frac{3}{2}}}$

$\mathsf {\frac{dy}{dx} = -\frac{3}{2x\sqrt{x}}}$

Question 5 :

$\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{x^{3}}{4})}$

$\mathsf {\frac{dy}{dx} = \frac{1}{4}(3)x^{3-1}}$

$\mathsf {\frac{dy}{dx} = \frac{3}{4}x^{2}}$

Question 6 :

$\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{5})}$

$\mathsf {\frac{dy}{dx} = 3(5)x^{5-1}}$

$\mathsf {\frac{dy}{dx} = 15x^{4}}$