Question

Differentiate w. r. t. x :-
(x³ – 2x - 1)⁵
​

Answer 1

Answer:

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Answer 2

The answer of this question is $5[3x^{2} -2](x^{3}-2x-1 )^{4}$.

Step-by-step explanation:

We are given ,

$(x^{3}-2x-1 )^{5}$

and we have to find the differentiation of given term w.r.t x.

• Formula used

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

This is the formula for differentiation w.r.t to x.

• Differentiation w.r.t x,

$\frac{d}{dx} (x^{3}-2x-1 )^{5}$

as our term is not simple it has itself a equation inside it so first we differentiate overall term then differentiate terms which are inside the bracket.

Here the value $n=5$ ,by using formula we get,

$5*(x^{3}-2x-1) ^{5-1} *[\frac{d}{dx} x^{3} -\frac{d}{dx}2x-\frac{d}{dx} 1]$

n for terms which are inside the bracket,

$n=3$ for $x^{3}$

$n=1$  for $2x$

$n=0$ for 1  as the differentiation of constant is zero.

$5(x^{3}-2x-1 )^{4}[3*x^{3-1} -2*1*x^{1-1}-0]$

$5(x^{3}-2x-1 )^{4}[3x^{2} -2x^{0}-0]$

$5(x^{3}-2x-1 )^{4}[3x^{2} -2]$

so the answer of this question is $5[3x^{2} -2](x^{3}-2x-1 )^{4}$.