If y=( x)^ x , then d y d x is equal to - Vidyadip

MCQ

If $y=(\tan x)^{\sin x}$, then $\frac{d y}{d x}$ is equal to

A
$\sec x+\cos x$
B
$\sec x+\log \tan x$
C
$(\tan x)^{\sin x}$
✓
None of these

✓

Answer

Correct option: D.

None of these

(d) : We have, $y=(\tan x)^{\sin x}$
Taking $\log$ on both sides, we get
$\log y=\sin x \log (\tan x)$
Differentiating w.r.t. $x$, we get
$
\begin{aligned}
\frac{1}{y} \frac{d y}{d x} & =\frac{\sin x}{\tan x} \cdot \sec ^2 x+\cos x \log (\tan x) \\
& =(\tan x)^{\sin x}[\sec x+\cos x(\log \tan x)]
\end{aligned}
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Continuity and Differentiability→Continuity and Differentiability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\int_{}^{} {\frac{{{x^3} - x - 2}}{{(1 - {x^2})}}\;dx = } $

The corner points of the feasible region determined by the following system of linear inequalities:

2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5).

Let Z = px + qy, where p.q > 0.

Condition on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is:

P = q
p = 2q
p = 3q
q = 3q

If the system of equations

$x+y+z=2$

$2 x+4 y-z=6$

$3 x+2 y+\lambda z=\mu$ has infinitely many solutions, then

If $\left|\begin{array}{cc}x & 2 \\ 15 & x\end{array}\right|=\left|\begin{array}{ll}6 & 6 \\ 3 & 4\end{array}\right|$ then $x=$ _________.

The value of $\frac{0.76\times0.76\times0.76+0.24\times0.24\times0.24}{0.76\times0.76-0.76\times0.24+ 0.24+0.24}$is:

$\int_{\, - 1/2}^{\,1/2} {(\cos x)\,\left[ {\log \left( {\frac{{1 - x}}{{1 + x}}} \right)} \right]\,dx = } $

The area of the triangle whose vertices are $(3,5)$, $(2,2)$ and $(k, 2)$ is 3 sq. unit then, value of $k$ is __________ .

If the co-ordinates of $A$ and $B$ be $(1, 2, 3)$ and $(7, 8, 7)$, then the projections of the line segment $AB$ on the co-ordinate axes are

Let $l_{1}$ be the line in $xy$-plane with $x$ and $y$ intercepts $\frac{1}{8}$ and $\frac{1}{4 \sqrt{2}}$ respectively, and $l_{2}$ be the line in $zx$-plane with $x$ and $z$ intercepts $-\frac{1}{8}$ and $-\frac{1}{6 \sqrt{3}}$ respectively. If $d$ is the shortest distance between the line $l_{1}$ and $l_{2}$, then $d ^{-2}$ is equal to

If $\int_{}^{} {\ln ({x^2} + x)dx = x\ln ({x^2} + x) + A} $, then $A = $