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The derivative of sin (x^2 with respect to x^3 is Single correct option
The derivative of
sin ( x 2 ) \sin(x^2) sin ( x 2 ) with respect to
x 3 x^3 x 3 is
A. 2 x cos ( x 2 ) 2x\cos(x^2) 2 x cos ( x 2 ) B. cos ( x 2 ) 3 x \frac{\cos(x^2)}{3x} 3 x c o s ( x 2 ) C. 2 cos ( x 2 ) 3 x 2 \frac{2\cos(x^2)}{3x^2} 3 x 2 2 c o s ( x 2 ) D. 2 cos ( x 2 ) 3 x \frac{2\cos(x^2)}{3x} 3 x 2 c o s ( x 2 ) Show answer and solution Answer: (D) 2 cos ( x 2 ) 3 x \frac{2\cos(x^2)}{3x} 3 x 2 c o s ( x 2 )
d d ( x 3 ) sin x 2 = d d x sin x 2 d d x x 3 = 2 x cos x 2 3 x 2 = 2 cos x 2 3 x \frac{d}{d(x^3)}\sin x^2=\frac{\frac{d}{dx}\sin x^2}{\frac{d}{dx}x^3}=\frac{2x\cos x^2}{3x^2}=\frac{2\cos x^2}{3x} d ( x 3 ) d sin x 2 = d x d x 3 d x d s i n x 2 = 3 x 2 2 x c o s x 2 = 3 x 2 c o s x 2 . The option
2 x cos ( x 2 ) 2x\cos(x^2) 2 x cos ( x 2 ) is the derivative with respect to
x x x , and
2 cos x 2 3 x 2 \frac{2\cos x^2}{3x^2} 3 x 2 2 c o s x 2 forgets to cancel one power of
x x x .
Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake