Answer
Verified
427.8k+ 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
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
What organs are located on the left side of your body class 11 biology CBSE
English Education in India was introduced on the advice class 11 social science CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Give two reasons to justify a Water at room temperature class 11 chemistry CBSE
Distinguish between Mitosis and Meiosis class 11 biology CBSE
This is an example of a very old viable seed excavated class 11 biology CBSE