Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 11

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Let $f (x) = x + 3 \ln (x - 2) and g (x) = x + 5 \ln (x - 1)$ , then the set of $x$ satisfying the inequality $f^{'} (x) < g^{'} (x)$ is -

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Important Questions on Differential Coefficient

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 12

Differential coefficient of

{(x^{\frac{l + m}{m - n}})}^{\frac{1}{n - l}} \cdot {(x^{\frac{m + n}{n - l}})}^{\frac{1}{l - m}} \cdot {(x^{\frac{n + l}{l - m}})}^{\frac{1}{m - n}}

w.r.t.

x

is -

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 13

If

y = \frac{1}{1 + x^{n - m} + x^{p - m}} + \frac{1}{1 + x^{m - n} + x^{p - n}} + \frac{1}{1 + x^{m - p} + x^{n - p}}

then

\frac{d y}{d x}

at

x = e^{m^{n^{p}}}

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 14

If

\cos^{- 1} (\frac{x^{2} - y^{2}}{x^{2} + y^{2}}) = \log a

then

\frac{d y}{d x} =

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 15

If

f (x) = \prod_{n = 1}^{100} {(x - n)}^{n (101 - n)};

then

\frac{f (101)}{f^{'} (101)} =

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 16

If

f (x) = {(|x|)}^{|\sin x|}

, then

f^{'} (- \frac{π}{4})

is -

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 17

If

y = \frac{x}{a + \frac{x}{b + \frac{x}{a + . . . . . . . . . . \infty}}}

then

\frac{d y}{d x}

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 18

If

y = x^{x^{2}}

then

\frac{d y}{d x} =

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Beta Question Bank for Engineering: Mathematics>Chapter 28 - Differential Coefficient>EXERCISE-1>Q 19

If

x^{m} \cdot y^{n} = (x + y)^{m + n}

, then

\frac{d y}{d x}

is -