RBSE Class 12 Maths Solutions Chapter 5 Continuity and Differentiability Ex 5.4

RBSE Class 12 Maths Solutions Chapter 5 Continuity and Differentiability Ex 5.4

Question 1.

$\frac{e^x}{\sin x}$
Answer:
Let y = $\frac{e^x}{\sin x}$
Differentiating both sides w.r.t. x, we get

Question 2.
esin -1 x
Answer:
Let y = esin -1 x
Differentiating both sides w.r.t. x, we get

Question 3.
ex3
Answer:
Let y = ex3
Differentiating both sides w.r.t. x, we get
$\frac{dy}{dx}$ = ex3 . $\frac{d}{dx}$(x3)
∴ $\frac{dy}{dx}$(ex2) = ex3 (3x2)

Question 4.
sin (tan-1 e-x)
Answer:
Let y = sin (tan-1 e-x)
Differentiating both sides w.r.t. x, we get

Question 5.
log cos(ex)
Answer:
Let y = log cos(ex)
Differentiating both sides w.r.t. x, we get

Question 6.
ex + ex2 + ex3 + ex4 + ex5
Answer:
Let y = ex + ex2 + ex3 + ex4 + ex5
Differentiating both sides w.r.t. x, we get

Question 7.

$\sqrt{e^{\sqrt{x}}}$, x > 0
Answer:
Let y = $\sqrt{e^{\sqrt{x}}}$
Differentiating both sides w.r.t. x, we get

Question 8.
log (log x), x > 1
Answer:
Let y = log(log x)
Differentiating both sides w.r.t. x, we get

Question 9.
$\frac{\cos x}{\log x}$, x > 0
Answer:
Let y = $\frac{\cos x}{\log x}$
Differentiating both sides w.r.t. x, we get

Question 10.
cos (log x + ex)
Answer:
Let y = cos (log x + ex)
Differentiating both sides w.r.t. x, we get

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