Differentiate: (x^2-4 x+5 ) (x^3-2 ). - Vidyadip

Question

Differentiate: $\left(x^2-4 x+5\right)\left(x^3-2\right)$.

✓

Answer

To find: Differentiation of $\left(x^2-4 x+5\right)\left(x^3-2\right)$
Formula used: (i) (uv)′ = u′v + uv′ (Using Leibnitz or product rule)
(ii) $\frac{d x^n}{d x}=n x^{n-1}$
Let $u =\left( x ^2-4 x +5\right)$ and $v =\left( x ^3-2\right)$
$\begin{aligned} u^{\prime} & =\frac{d u}{d x}=\frac{d\left(x^2-4 x+5\right)}{d x}=2 x-4 \\ v^{\prime} & =\frac{d v}{d x}=\frac{d\left(x^3-2\right)}{d x}=3 x^2\end{aligned}$
Put the above obtained values in the formula:-
(uv)′ = u′v + uv′
$\left[\left(x^2-4 x+5\right)\left(x^3-2\right)\right]^{\prime}=(2 x-4) \times\left(x^3-2\right)+\left(x^2-4 x+5\right) \times\left(3 x^2\right)$
$\begin{array}{l}=2 x^4-4 x-4 x^3+8+3 x^4-12 x^3+15 x^2 \\ =5 x^4-16 x^3+15 x^2-4 x+8 .\end{array}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "2 Marks Questions" from Model Paper 10→Model Paper 10 — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Similar questions

For any two sets A and B, prove that.
$\text{B}\subset\text{A}\cup\text{B}.$

Prove that:
$\tan(-225^\circ)\cot(-405^\circ)-\tan(765^\circ)+\cot(675^\circ)=0$

Find the indicated terms of the sequence, whose nth term is $a _ { n } = \frac { n ( n - 2 ) } { n + 3 }$; a₂₀

Write the following relations as sets of ordered pairs and find which of them are functions:
$\{(\text{x},\text{y}):\text{y}=3\text{x},\text{x}\in\{1,2,3\},\text{y}\in\{3,6,9,12\}\}$

How many 9-digit numbers of different digits can be formed?

Evaluate $\lim _{x \rightarrow 0} \frac{e^{k x}-1}{x}$.

Find the value of tan 15^o

Write the following functions in the form of ordered pairs and also write their range.
(i) $f: A \rightarrow R , f(x)=x^2+1$
Where $A=\{-3,-2,-1,0,1,2,3\}$
(ii) $g: B \rightarrow I , g(x)=x^2-x$
Where $B =\{x: x \in N , x \leq 5\}$

Find the equation of the line which passes through the point (3, 4) and is such that the portion of it intercepted between the axes is divided by the point in the ratio 2 : 3.

Find the sum of the following series to infinity:

$\frac{2}{5}+\frac{3}{5^2}+\frac{2}{5^3}+\frac{3}{5^4}+\ ... \infty$