Question

1. Differentiate the following, where \( a, b \) and \( c \) are constants, with respect to \( x \) : (i) \( \left(3 x^{2}-4\right)^{5} \) (ii) \( \sqrt[3]{2 x^{3}+7} \) (iii) \( \left(a x^{2}+b x\right)^{6} \) (iv) \( \frac{1}{3 \sqrt{x^{2}-3}} \) (v) \( \left(2 x^{2}-\frac{5}{x}\right)^{6} \) (vi) \( \frac{3}{\sqrt{a^{2}-b x^{2}}} \) vii) \( \frac{2 x-5}{3 x+7} \) (vii) \( \frac{\sqrt{x+1}}{x^{2}-4} \) (ix) \( \frac{3 x-7}{\sqrt{2 x+9}} \) (2) i) \( e^{\tan 3 x} \sin 3 x \) ii) \( e^{\sin x} \cos \frac{1}{2} x \) iii) \( e^{x}(\cos x+\sin x) \) iv) \( x^{2} e^{\cos x} \) \( \checkmark \ln (\sin x) \) vi ) \( x^{2} \ln (\cos x) \) vii) \( \frac{\sin 3 x}{e^{2 x-1}} \) viii) \( \frac{e^{4 x} \tan x}{\ln x} \)

          1. Differentiate the following, where \( a, b \) and \( c \) are constants, with respect to \( x \) :
(i) \( \left(3 x^{2}-4\right)^{5} \)
(ii) \( \sqrt[3]{2 x^{3}+7} \)
(iii) \( \left(a x^{2}+b x\right)^{6} \)
(iv) \( \frac{1}{3 \sqrt{x^{2}-3}} \)
(v) \( \left(2 x^{2}-\frac{5}{x}\right)^{6} \)
(vi) \( \frac{3}{\sqrt{a^{2}-b x^{2}}} \)
vii) \( \frac{2 x-5}{3 x+7} \)
(vii) \( \frac{\sqrt{x+1}}{x^{2}-4} \)
(ix) \( \frac{3 x-7}{\sqrt{2 x+9}} \)
(2) i) \( e^{\tan 3 x} \sin 3 x \)
ii) \( e^{\sin x} \cos \frac{1}{2} x \)
iii) \( e^{x}(\cos x+\sin x) \)
iv) \( x^{2} e^{\cos x} \)
\( \checkmark \ln (\sin x) \)
vi ) \( x^{2} \ln (\cos x) \)
vii) \( \frac{\sin 3 x}{e^{2 x-1}} \)
viii) \( \frac{e^{4 x} \tan x}{\ln x} \)

1. Differentiate the following, where a, b and c are constants, with respect to x :
(i) (3 x^2-4)^5
(ii) √(2 x^3+7)
(iii) (a x^2+b x)^6
(iv) (1)/(3 √(x^2-3))
(v) (2 x^2-(5)/(x))^6
(vi) (3)/(√(a^2-b x^2))
vii) (2 x-5)/(3 x+7)
(vii) (√(x+1))/(x^2-4)
(ix) (3 x-7)/(√(2 x+9))
(2) i) e^tan 3 xsin 3 x
ii) e^sin xcos(1)/(2) x
iii) e^x(cos x+sin x)
iv) x^2 e^cos x
ln (sin x)
vi ) x^2ln (cos x)
vii) (sin 3 x)/(e^2 x-1)
viii) (e^4 xtan x)/(ln x)

Added by Jennifer D.

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