Differentiate the following function with respect to (x): (x^3+1)… - Vidyadip

Question

Differentiate the following function with respect to $(\text{x})$:$\frac{(\text{x}^3+1)(\text{x}-2)}{\text{x}^2}$

✓

Answer

We have,$\frac{\text{d}}{\text{dx}}\frac{(\text{x}^3+1)(\text{x}-2)}{\text{x}^2}$
$=\frac{\text{d}}{\text{dx}}\frac{(\text{x}^4-\text{2x}^3+\text{x}-2)}{\text{x}^2}$
$=\frac{\text{d}}{\text{dx}}(\text{x}^2-2\text{x}+\text{x}^{-1}-\text{2x}^{-2})$
$=\frac{\text{d}}{\text{dx}}(\text{x}^2)-2\frac{\text{d}}{\text{dx}}(\text{x})+\frac{\text{d}}{\text{dx}}(\text{x}^{-1})-2\frac{\text{d}}{\text{dx}}(\text{x}^{-2})$
$=\text{2x}-2-\frac{1}{\text{x}^2}+2.\frac{2}{\text{x}^3}$
$=\text{2x}-2-\frac{1}{\text{x}^2}+\frac{4}{\text{x}^3}$

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 "3 Marks Question" from Derivatives→Derivatives — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Find the lengths of the medians of the triangle with vertices $A (0, 0, 6), B (0, 4, 0)$ and $C (6, 0, 0).$

Find the standard deviation for the following data:

$x_i$	$3$	$8$	$13$	$18$	$23$
$f_i$	$7$	$10$	$15$	$10$	$6$

Solve the following linear inequations in R:
$\frac{\text{x}-1}{\text{x}+3}>2$

If $^nC_{10} =\ ^nC_{12},$ Find $^{23}C_n.$

Find the domain of the following real valued functions of real variable:
$\text{f(x)}=\frac{1}{\text{x}-7}$

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and $100$ m long is supported by vertical wires attached to the cable, the longest wire being $30$ m and the shortest being $6$ m. Find the length of a supporting wire attached to the roadway $18$ m from the middle.

Prove that: $\tan13\text{x}-\tan9\text{x}-\tan4\text{x}=\tan13\text{x}\tan9\text{x}\tan4\text{x}$

Differentiate the following from first principle:$\text{x}^3-\text{5x}^2+\text{x}-5$

Find the distance between the following pairs of points:
$(i) (2, 3, 5)$ and $(4, 3, 1)$
$(ii) (-3, 7, 2)$ and $(2, 4, -1)$
$(iii) (-1, 3, -4)$ and $(1, -3, 4)$
$(iv) (2, -1, 3)$ and $(-2, 1, 3)$

If $e$ and $e^{\prime}$ be the eccentricity of a hyperbola and its conjugate, then prove that $\frac{1}{e^2}+\frac{1}{\left(e^{\prime}\right)^2}=1$.