Test Index

KCET 2021 Math Solved Paper

© examsnet.com

Question : 42 of 60

Marks: +1, -0

If

y=(x-1)^{2}(x-2)^{3}(x-3)^{5}

\frac{dy}{dx}

x=4

is equal to

108
54
36
516

Solution:

y=(x-1)^{2}(x-2)^{3}(x-3)^{5}

Taking log on both sides,

⇒

\log y=\log [(x-1)^{2}(x-2)^{3}(x-3)^{5}]

\log y=2 \log (x-1)+3 \log (x-2)+5 \log (x-3)

On both sides differentiating w.r.t.

x

, we get

\frac{1}{y} \frac{dy}{dx} = \frac{2}{x-1} + \frac{3}{x-2} + \frac{5}{x-3}

⇒

\frac{dy}{dx} = (x-1)^{2}(x-2)^{3}(x-3)^{5}

\left[ \frac{2}{x-1} + \frac{3}{x-2} + \frac{5}{x-3} \right]

∴

\left(\frac{dy}{dx}\right)_{x=4} = 3^{2} \times 2^{3} \times 1^{3} \left[ \frac{2}{3} + \frac{3}{2} + 5 \right]

=9 \times 8 \times \left(\frac{4+9+30}{6}\right)=516

© examsnet.com

Go to Question:

Prev Question

Next Question