If y= [ (x^5 ) ] then find d y d x - Vidyadip

Question

If $y=\log \left[\cos \left(x^5\right)\right]$ then find $\frac{ d y}{ d x}$

✓

Answer

$y=\log \left[\cos \left(x^5\right)\right]$
Differentiating w.r.t. $x$, we get
$ \frac{ d y}{ d x}=\frac{ d }{ d x}\left[\log \left\{\cos \left(x^5\right)\right\}\right]$
$=\frac{1}{\cos \left(x^5\right)} \cdot \frac{ d }{ d x}\left[\cos \left(x^5\right)\right]$
$=\frac{1}{\cos \left(x^5\right)} \cdot\left[-\sin \left(x^5\right)\right] \cdot \frac{ d }{ d x}\left(x^5\right)$
$=\frac{-\sin \left(x^5\right)}{\cos \left(x^5\right)} \cdot 5 x^4$
$=-5 x^4 \tan \left(x^5\right) $

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 "Solve the Following Question.(2 Marks)" from Question Bank [2022]→Question Bank [2022] — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Verify Lagrange’s mean value theorem for the following functions: f(x) = log x on [1, e].

Find the adjoint of matrix $A=\left[\begin{array}{cc}2 & -3 \\ 4 & 1\end{array}\right]$

Find the values of x for which the following functions are strictly increasing:

$f(x)=x^3-6 x^2-36 x+7$

If $\log _{10}\left(\frac{x^2-y^3}{x^3+y^3}\right)=2$, show that $\frac{d y}{d x}=-\frac{99 x^2}{101 y^2}$

Find the area of the region bounded by the line $2 y+x=8$, $x$-axis and the lines $x=2$ and $x=4$.

Write the total number of binary operations on a set consisting of two elements.

Write the value of the area of the parallelogram determined by the vectors $2\hat{\text{i}}$ and $3\hat{\text{j}}.$

Integrate the following functions w. r. t. x

$\int \frac{1}{3+2 \sin x-\cos x} \cdot d x$

If $\text{A}=\text{diag}\begin{pmatrix}2&-5&9\end{pmatrix},\text{ B}=\text{diag}\begin{pmatrix}1&1&-4\end{pmatrix}$ and $\text{C}=\text{diag}\begin{pmatrix}-6&3&4\end{pmatrix},$ find.
A - 2B

Integrate the following functions w.r.t x:

$\tan ^5 x$