Question

If y=e^ax 〖cos〗^3 x〖sin〗^2 x find dy/dx.

Answer 1

Question 34423

We are given $y(x) = e^{ax} \cos^3 x \sin^2 x$ . Using Leibniz rule for differentiation, obtain

$$\frac {d y}{d x} = a e ^ {a x} \cos^ {3} x \sin^ {2} x - 3 e ^ {a x} \cos^ {2} x \sin^ {3} x + 2 e ^ {a x} \cos^ {4} x \sin x = e ^ {a x} \cos^ {2} x \sin x [ \cos x \sin x - 3 \sin^ {2} x + 2 \cos^ {2} x ]$$