Question

Find first derivative f(x)= x² - 4 /x³ + 9 ​

Answer 1

Answer:

$f'(x)=2x+\dfrac{12}{x^4}$

Step-by-step explanation:

$f(x)=x^2-\dfrac{4}{x^3}+9$

Apply exponent rule $\dfrac{1}{a^b}=a^{-b}$:

$\implies f(x)=x^2-4x^{-3}+9$

Differentiate using the power rule $\frac{d}{dx}(x^a)=a \cdot x^{a-1}$ :

$\implies f'(x)=2 \cdot x^{2-1}-(-3)4x^{-3-1}+0$

$\implies f'(x)=2x+12x^{-4}$

$\implies f'(x)=2x+\dfrac{12}{x^4}$

Answer 2

Answer:

f'(x) = 2x + $\frac{12}{x^{4} }$

Step-by-step explanation:

differentiate using the power rule

$\frac{d}{dx}$ ( a$x^{n}$ ) = na$x^{n-1}$

Given

f(x) = x² - $\frac{4}{x^3}$ + 9 = x² - 4$x^{-3}$ + 9 , then

f'(x) = 2x + 12$x^{-4}$ = 2x + $\frac{12}{x^{4} }$