The derivative of the function \( f(x) = \cos^3(x) \cdot \sin(x) \) is calculated using the product rule and chain rule. The correct application of the formula \( \frac{d(uv)}{dx} = u \frac{dv}{dx} + v \frac{du}{dx} \) yields \( \frac{d}{dx}(\cos^3(x) \cdot \sin(x)) = -3\sin^2(x)\cos^2(x) + \cos^4(x) \). The derivatives \( \frac{dv}{dx} = -3\sin(x)\cos^2(x) \) and \( \frac{du}{dx} = \cos(x) \) are correctly identified. This confirms the final result is accurate.
PREREQUISITESStudents in calculus courses, mathematics educators, and anyone looking to strengthen their understanding of differentiation techniques involving trigonometric functions.
It is against Physics Forums policy to provide answers to posters' questions.omkar13 said:I think the question is ((cosx)^3)*sin(x).Am I right?The formula for d(uv)/dx=u(dv/dx)+v(du/dx).And of course I think you need only formula.Do you need answer?