Let y=2^cos^2x ∴ log y=log(2^cos^2x)=cos^2x.log 2 On diffrentiating w.r.t x, we get 1/y.dy/dx=log 2.d/dx(cos x)^2 ⇒1/y.dy/dx=log2.[2cos x].d/dx(cos x) =log 2. ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Inequalities of Integrals

Find d/d x2co...

Question

$F i n d \frac{d}{d x} (2^{c o s^{2} x})$

Open in App

Solution

Let $y = 2^{c o s^{2} x}$
$∴ l o g y = l o g (2^{c o s^{2} x}) = c o s^{2} x . l o g 2$

On diffrentiating w.r.t x, we get
$\frac{1}{y} . \frac{d y}{d x} = l o g 2. \frac{d}{d x} (c o s x)^{2} \Rightarrow \frac{1}{y} . \frac{d y}{d x} = l o g 2. [2 c o s x] . \frac{d}{d x} (c o s x) = l o g 2. 2. c o s x . (- s i n x) = l o g 2. (- s i n 2 x) ∴ \frac{d y}{d x} = - y . (s i n 2 x) l o g 2$

Suggest Corrections

Similar questions

Q. If 4 : 6 : : 8 : d, then find d.

Q. In an AP:
(i) Given

a = 5, d = 3

a_{n} = 50

, find

n

and

S_{n}

.
(ii) Given

a = 7

a_{13} = 35

, find

d

and

S_{13}

.
(iii) Given

a_{12} = 37

d = 3

, find

a

and

S_{12}

.
(iv) Given

a_{3} = 15

S_{10} = 125

, find

d

and

a_{10}

.
(v) Given

d = 5

S_{9} = 75

, find

a

and

a_{9}

.
(vi) Given

a = 2, d = 8

S_{n} = 90

, find

n

and

a_{n}

.
(vii) Given

a = 8

a_{n} = 62

S_{n} = 210

, find

n

and

d

.
(viii) Given

a_{n} = 4

d = 2

S_{n} = - 14

, find

n

and

a

.
(ix) Given

a = 3, n = 8, S = 192

, find

d

.
(x) Given

l = 28, S = 144

, and there are total 9 terms. Find

a

Q. Find

\frac{d y}{d x}

y = x^{x}

Q. Find

\frac{d}{d x} {sin}^{3} 4 x {cos}^{8} 5 x

Q. Find

\frac{d}{d x} (x^{3} {log}_{e} x)

Join BYJU'S Learning Program

Find ddx(2cos2x)

Let y=2cos2x ∴ log y=log(2cos2x)=cos2x.log 2 On diffrentiating w.r.t x, we get 1y.dydx=log 2.ddx(cos x)2⇒1y.dydx=log2.[2cos x].ddx(cos x)=log 2. 2.cos x.(−sin x)=log 2. (−sin2 x)∴ dydx=−y.(sin 2x) log 2

$F i n d \frac{d}{d x} (2^{c o s^{2} x})$