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

Rajasthan Board RBSE Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability Ex 5.4 Textbook Exercise Questions and Answers.

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.
e^{sin -1 x}
Answer:
Let y = e^{sin -1 x}
Differentiating both sides w.r.t. x, we get

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

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

Question 6.
e^x + e^x2 + e^x3 + e^x4 + e^x5
Answer:
Let y = e^x + e^x2 + e^x3 + e^x4 + e^x5
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 + e^x)
Answer:
Let y = cos (log x + e^x)
Differentiating both sides w.r.t. x, we get