Answer

Verified

454.8k+ views

Hint: you can differentiate it by using formulae of logarithm or

Using substitution method.

We have to differentiate it with respect to $x$.

We will use a substitution method.

Let, $\tan x = t$

$\begin{gathered}

\therefore y = \log t \\

dy = \frac{1}{t}dt \\

\end{gathered} $

$\frac{{dy}}{{dt}} = \frac{1}{t} = \frac{1}{{\tan x}}$$ \ldots \ldots \left( 1 \right)$

Now

$\begin{gathered}

t = \tan x \\

dt = {\sec ^2}xdx \\

\frac{{dt}}{{dx}} = {\sec ^2}x \ldots \ldots \left( 2 \right) \\

\end{gathered} $

On multiplying equation $\left( 1 \right)$and $\left( 2 \right)$

We get,

$\begin{gathered}

\frac{{dy}}{{dt}} \times \frac{{dt}}{{dx}} = \frac{{{{\sec }^2}x}}{{\tan x}} \\

\frac{{dy}}{{dx}} = \frac{{\cos x}}{{\cos x.\cos x.\sin x}} = \frac{1}{{\sin x.\cos x}} \\

\frac{{dy}}{{dx}} = \frac{1}{{\sin x.\cos x}} \\

\end{gathered} $

Is the required answer.

Note:Using a substitution method you can solve easily. You have to find

Differentiation with respect to $x$, then you can differentiate it with respect

to $t$ and further differentiate $t$ with respect to $x$

Using substitution method.

We have to differentiate it with respect to $x$.

We will use a substitution method.

Let, $\tan x = t$

$\begin{gathered}

\therefore y = \log t \\

dy = \frac{1}{t}dt \\

\end{gathered} $

$\frac{{dy}}{{dt}} = \frac{1}{t} = \frac{1}{{\tan x}}$$ \ldots \ldots \left( 1 \right)$

Now

$\begin{gathered}

t = \tan x \\

dt = {\sec ^2}xdx \\

\frac{{dt}}{{dx}} = {\sec ^2}x \ldots \ldots \left( 2 \right) \\

\end{gathered} $

On multiplying equation $\left( 1 \right)$and $\left( 2 \right)$

We get,

$\begin{gathered}

\frac{{dy}}{{dt}} \times \frac{{dt}}{{dx}} = \frac{{{{\sec }^2}x}}{{\tan x}} \\

\frac{{dy}}{{dx}} = \frac{{\cos x}}{{\cos x.\cos x.\sin x}} = \frac{1}{{\sin x.\cos x}} \\

\frac{{dy}}{{dx}} = \frac{1}{{\sin x.\cos x}} \\

\end{gathered} $

Is the required answer.

Note:Using a substitution method you can solve easily. You have to find

Differentiation with respect to $x$, then you can differentiate it with respect

to $t$ and further differentiate $t$ with respect to $x$

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Simon Commission came to India in A 1927 B 1928 C 1929 class 11 social science CBSE

One cusec is equal to how many liters class 8 maths CBSE

What organs are located on the left side of your body class 11 biology CBSE

Lamps used for street lighting are connected in AParallel class 11 physics CBSE

What is the type of food and mode of feeding of the class 11 biology CBSE

Proton was discovered by A Thomson B Rutherford C Chadwick class 11 chemistry CBSE

Check whether the given numbers are divisible by 11 class 6 maths CBSE