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NCERT Class 12 Maths Chapter 5: Continuity And Differentiability 18 Questions Solved

NCERT Solutions for Class 12 Maths Chapter 5 Continuity And Differentiability — Exercise 5.5

Click any question below for its step-by-step NCERT textbook solution, concept hints, and worked explanation.

Differentiate \(\cos{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(3 x \right)}\) with respect to x; on R.

Differentiate \(\sqrt{\frac{\left(x - 2\right) \left(x - 1\right)}{\left(x - 5\right) \left(x - 4\right) \left(x - 3\right)}}\) with…

Differentiate \(\log{\left(x \right)}^{\cos{\left(x \right)}}\) with respect to x; for x>1.

Differentiate \(- 2^{\sin{\left(x \right)}} + x^{x}\) with respect to x; for x>0.

Differentiate \(\left(x + 3\right)^{2} \left(x + 4\right)^{3} \left(x + 5\right)^{4}\) with respect to x; on R.

Differentiate \(x^{1 + \frac{1}{x}} + \left(x + \frac{1}{x}\right)^{x}\) with respect to x; for x>0.

Differentiate \(x^{\log{\left(x \right)}} + \log{\left(x \right)}^{x}\) with respect to x; for x>1.

Differentiate \(\sin^{x}{\left(x \right)} + \operatorname{asin}{\left(\sqrt{x} \right)}\) with respect to x; for 0<x<1.

Differentiate \(x^{\sin{\left(x \right)}} + \sin^{\cos{\left(x \right)}}{\left(x \right)}\) with respect to x; where x>0 and sin x>0.

Differentiate \(x^{x \cos{\left(x \right)}} + \frac{x^{2} + 1}{x^{2} - 1}\) with respect to x; for x>0, x≠1.

Differentiate \(\left(x \sin{\left(x \right)}\right)^{\frac{1}{x}} + \left(x \cos{\left(x \right)}\right)^{x}\) with respect to x…

Find dy/dx if xʸ+yˣ=1.

Find dy/dx if yˣ=xʸ.

Find dy/dx if (cos x)ʸ=(cos y)ˣ.

Find dy/dx if xʸ=e^(x−y).

Differentiate f(x)=(1+x)(1+x²)(1+x⁴)(1+x⁸) and find f′(1).

Differentiate (x²−5x+8)(x³+7x+9) by (i) product rule, (ii) expansion, (iii) logarithmic differentiation. Compare.

Show (uvw)′=u′vw+uv′w+uvw′ by repeated product rule and logarithmic differentiation.