Question

Let $f(x)=-9x^{-4}$ find$f'(2x)$

Answer 1

$\sf f(x) = -9x^{-4}$

Differentiate with respect to x

$\sf f'(x) = -9(-4)x^{-5}$

$\sf f'(x) = 36x^{-5}$

For finding f'(2x), substitue 2x instead of x

$\sf f'(2x) = 36(2x)^{-5}$

$\sf f'(2x) = \frac{36}{32}\times x^{-5}$

$\sf f'(2x) = \frac{9}{8x^5}$

Properties used :

y = xⁿ

Then, dy/dx = nxⁿ- ¹

Answer 2

Required Answer :

$\tt f (x) = -9x^{-4}$

Deferentivete with x ,

$\tt f' (x) = -9 (-4) x^{-5}$

$\tt \: f'(x) = 36x^{-5}$

For finding f'(2x) , we should substitute 2x insted of x

$➙\tt f'(2x) = 36 (2x) ^{-5}$

$➙\tt f'(2x) = 36/32 × x^{-5}$

$➙\tt f' (2x) = 9/(8×5 )$

The propertie we have used is

y = xⁿ

Then, dy/dx = nxⁿ- ¹