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Home
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NUST Entrance Test
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Mathematics
/
Differentiation

Set 1

MM

Mashaal Masha

Oct 05, 2022

On this page

$Derivate of $\sin(x)$ is$
$\frac{d(0)}{dx}=$
$Which of the following mathematician gave the notation $D \space f(x)$ for the derivative?$
$Differentiate $\sin(2x)$ with respect to x$
$For which of the following intervals is the function $y=x^{2}-6x+5$ increasing?$
$Differentiate $\ln (e)$ with respect to $x$$
$What is the derivative of $\tan(\sqrt x)$$
$Derivative of ${\rm{cose}}{{\rm{c}}^{ - 1}}\left( x \right)$ is$
$The derivative of $f(x)$ with respect to $x$ is defined as$
$Find the derivative of $3^{2x}$$

Choose the correct options for the following questions.

Derivate of $\sin(x)$ is

Difficulty: Easy

A:

-\cos(x)

B:

\cos(x)

C:

{\rm{cose}}{{\rm{c}}}\left( x \right)

D:

-{\rm{cose}}{{\rm{c}}}\left( x \right)

View Solution Steps

\frac{d(0)}{dx}=

Difficulty: Easy

A:

Derivate of $\sin(x)$ is

B:

Constant

C:

Infinite

D:

None of these

View Solution Steps

Which of the following mathematician gave the notation $D \space f(x)$ for the derivative?

Difficulty: Easy

A:

Euler

B:

Newton

C:

Lagrange

D:

Cauchy

View Solution Steps

Differentiate $\sin(2x)$ with respect to x

Difficulty: Easy

A:

2\cos(2x)

B:

2\sin(2x)

C:

2\left(1-\sin^{2}(x)\right)

D:

Both A and C

View Solution Steps

For which of the following intervals is the function $y=x^{2}-6x+5$ increasing?

Difficulty: Easy

A:

$x>5$

B:

$x>3$

C:

$x<1$

D:

$1

View Solution Steps

Differentiate $\ln (e)$ with respect to $x$

Difficulty: Easy

A:

\frac{1}{e}

B:

$0$

C:

\frac{1}{x}

D:

$e$

What is the derivative of $\tan(\sqrt x)$

Difficulty: Easy

A:

\sec^{2}(\sqrt x)

B:

\frac{1}{\sqrt{2}} \sec^{2}(\sqrt x)

C:

\frac{1}{2\sqrt{x}} \sec^{2}(\sqrt x)

D:

\sec^{2}(\sqrt x) \tan \left(\frac{1}{2\sqrt x} \right)

View Solution Steps

Derivative of ${\rm{cose}}{{\rm{c}}^{ - 1}}\left( x \right)$ is

Difficulty: Easy

A:

- \frac{1}{{|x|\sqrt {{x^2} - 1} }}

B:

- \frac{1}{{|x|\sqrt {{x^2} + 1} }}

C:

\frac{1}{{|x|\sqrt {{x^2} - 1} }}

D:

- \frac{1}{{\sqrt {{x^2} - 1} }}

View Solution Steps

The derivative of $f(x)$ with respect to $x$ is defined as

Difficulty: Easy

A:

The rate of change of $f(x)$ with respect to $x$

B:

The increase in the relevance rate of $f(x)$ with respect to $x$

C:

The decrease in the relevance rate of $f(x)$ with respect to $x$

D:

None of these

View Solution Steps

Find the derivative of $3^{2x}$

Difficulty: Easy

A:

2\ln \left( 3 \right) \times {3^{2x}}

B:

\ln \left( 3 \right) \times {3^{2x}}

C:

\ln \left( 2 \right) \times {3^{2x}}

D:

2x \times {3^{2x}}

View Solution Steps

Differentiation - Set 1