If y=(x-1)^{2}(x-2)^{3}(x-3)^{5},then frac{dy | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given $y=(x-1)^{2}(x-2)^{3}(x-3)^{5}$.Taking the natural logarithm on both sides:$\log y = \log [(x-1)^{2}(x-2)^{3}(x-3)^{5}]$Using logarithmic pr

Vedclass · Accepted Answer

$516$

Vedclass · Answer

(D) Given $y=(x-1)^{2}(x-2)^{3}(x-3)^{5}$.Taking the natural logarithm on both sides:$\log y = \log [(x-1)^{2}(x-2)^{3}(x-3)^{5}]$Using logarithmic properties,$\log y = 2 \log (x-1) + 3 \log (x-2) + 5 \log (x-3)$.Differentiating both sides with respect to $x$:$\frac{1}{y} \frac{dy}{dx} = \frac{2}{x-1} + \frac{3}{x-2} + \frac{5}{x-3}$.Therefore,$\frac{dy}{dx} = y \left[ \frac{2}{x-1} + \frac{3}{x-2} + \frac{5}{x-3} ight]$.Substituting $x=4$:$y(4) = (4-1)^{2}(4-2)^{3}(4-3)^{5} = 3^{2} 	imes 2^{3} 	imes 1^{5} = 9 	imes 8 	imes 1 = 72$.$\left( \frac{dy}{dx} ight)_{x=4} = 72 \left[ \frac{2}{4-1} + \frac{3}{4-2} + \frac{5}{4-3} ight] = 72 \left[ \frac{2}{3} + \frac{3}{2} + 5 ight]$.$= 72 \left[ \frac{4 + 9 + 30}{6} ight] = 72 	imes \frac{43}{6} = 12 	imes 43 = 516$.

If $y=(x-1)^{2}(x-2)^{3}(x-3)^{5}$,then $\frac{dy}{dx}$ at $x=4$ is equal to

Similar Questions

If $y = \sqrt {\frac{{1 + x}}{{1 - x}}} ,$ then $\frac{{dy}}{{dx}} = $

$\text{If } \frac{d}{dx} \left( \frac{x^2+1}{(x^2+5)(x^2+9)} \right) = \frac{2x(x^2+1)}{(x^2+5)(x^2+9)} \left[ \frac{1}{f(x)} - \frac{1}{g(x)} - \frac{1}{h(x)} \right], \text{ then } 2h(x) - f(x) - g(x) = $

Differentiate the following with respect to $x$: $\cos x \cdot \cos 2x \cdot \cos 3x$

If $x^p \cdot y^q = (x + y)^{p + q}$,then $\frac{dy}{dx}$ is:

If $y=(\tan x)^{\sin x}$,then $\frac{dy}{dx}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module