\(\frac{d}{d x}\left(\frac{2}{\pi} \sin x^{\circ}\right)\) is

(a)

\({\pi\over 180}cos \ x^o\)

(b)

\({1\over 90} cos \ x^o\)

(c)

\({\pi\over 90}cos \ x^o\)

(d)

\({2\over \pi}cos \ x^o\)

If y = mx + c and f(0) =\(f '(0)=1\), then f(2) is

(a)

1

(b)

2

(c)

3

(d)

-3

\({d\over dx}(e^{x+5log \ x})\) is

(a)

e^x.x⁴(x+5)

(b)

e^x.x(x+5)

(c)

e^x\(+{5\over x}\)

(d)

e^x\(-{5\over x}\)

The differential coefficient of log₁₀ x with respect to log_x10 is

(a)

1

(b)

-(log₁₀ x)²

(c)

(log_x 10)²

(d)

\(x^2\over100\)

\(\text { If } f(x)= \begin{cases}x-5 & \text { if } x \leq 1 \\ 4 x^2-9 & \text { if } 1<x<2 \\ 3 x+4 & \text { if } x \geq 2\end{cases}\), then the right hand derivative of f(x) at x = 2 is

(a)

0

(b)

2

(c)

3

(d)

4

Choose the correct or the most suitable answer from the given four alternatives.
If f(x) = 4x⁸, then ________

(a)

\(f^{ ' }\left( \frac { 1 }{ 2 } \right) =f^{ ' }\left( \frac { -1 }{ 2 } \right) \)

(b)

\(f\left( \frac { 1 }{ 2 } \right) =-f^{ ' }\left( \frac { -1 }{ 2 } \right) \)

(c)

\(f\left( \frac { 1 }{ 2 } \right) =f\left( \frac { -1 }{ 2 } \right) \)

(d)

\(f\left( \frac { 1 }{ 2 } \right) =f^{ ' }\left( \frac { -1 }{ 2 } \right) \)

 Choose the correct or the most suitable answer from the given four alternatives.
If \(y=\log _{ a }{ x } \) then \(\frac { dy }{ dx } \) is ______

(a)

\(\frac { 1 }{ x } \)

(b)

\(\frac { 1 }{ x\log _{ e }{ a } } \)

(c)

\(\log { _{ e }^{ a } } \)

(d)

\(\frac { 1 }{ \log _{ a }{ x } } \)

Choose the correct or the most suitable answer from the given four alternatives.
The derivative of \(\cos ^{ -1 }{ (2{ x }^{ 2 } } -1)\) with respect to \(\cos ^{ -1 }{ x } \) is _____

(a)

2

(b)

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

(c)

\(\frac { 2 }{ x } \)

(d)

\(1-{ x }^{ 2 }\)

Choose the correct or the most suitable answer from the given four alternatives.
If \(y=\log \left(\frac{1-x^2}{1+x^2}\right)\) then \(\frac{dy}{dx}\) is ______

(a)

\(\frac { 4{ x }^{ 3 } }{ 1-{ x }^{ 4 } } \)

(b)

\(-\frac { 4x }{ 1-{ x }^{ 4 } } \)

(c)

\(\frac { 1 }{ 4-{ x }^{ 4 } } \)

(d)

\(\frac { -4{ x }^{ 3 } }{ 1-{ x }^{ 4 } } \)

Choose the correct or the most suitable answer from the given four alternatives.
If f(x) is an odd function, then  f^'(x) is an ______ function

(a)

even

(b)

odd

(c)

even or odd

(d)

neither even nor odd