Let gx - x5 lnfx where fx is adifferentiable positive function on 0- satisfying f3 - 1 and f-3 - 2 then g-3 is equal to

The correct option is D 486 Given, g(x) = x^5 ln(f(x)) Differentiating w.r.t .x we get, ⇒ g'(x) = 5x^4 . ln f(x) + x^5 f'(x)/f(x) Put #160;x ...

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Byju's Answer

Standard XII

Mathematics

Chain Rule of Differentiation

Let gx = x5...

Question

Let $g (x) = x^{5} ln (f (x))$ where $f (x)$ is adifferentiable positive function on $(0, \infty)$ satisfying $f (3) = 1$ and $f^{'} (3) = 2$ then $g^{'} (3)$ is equal to

243

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486

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Solution

The correct option is D $486$
Given, $g (x) = x^{5} ln (f (x))$
Differentiating w.r.t .x we get,
$\Rightarrow g^{'} (x) = 5 x^{4} . ln f (x) + \frac{x^{5} f^{'} (x)}{f (x)}$
Put $x = 3$
$\Rightarrow g^{'} (3) = 5. (3)^{4} ln (1) + 3^{5} .2 = 486$

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Similar questions

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Let g(x)=x5ln(f(x)) where f(x) is adifferentiable positive function on (0,∞) satisfying f(3)=1 and f′(3)=2 then g′(3) is equal to

The correct option is D 486Given, g(x)=x5ln(f(x))Differentiating w.r.t .x we get,⇒g′(x)=5x4.lnf(x)+x5f′(x)f(x)Put x=3⇒g′(3)=5.(3)4ln(1)+35.2=486

Let $g (x) = x^{5} ln (f (x))$ where $f (x)$ is adifferentiable positive function on $(0, \infty)$ satisfying $f (3) = 1$ and $f^{'} (3) = 2$ then $g^{'} (3)$ is equal to

The correct option is D $486$
Given, $g (x) = x^{5} ln (f (x))$
Differentiating w.r.t .x we get,
$\Rightarrow g^{'} (x) = 5 x^{4} . ln f (x) + \frac{x^{5} f^{'} (x)}{f (x)}$
Put $x = 3$
$\Rightarrow g^{'} (3) = 5. (3)^{4} ln (1) + 3^{5} .2 = 486$