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Popular >

derivative of xsin^2(2x)

Solution

derivative of

x sin^{2} (2 x)

Solution

sin^{2} (2 x) + 2 x sin (4 x)

Solution steps

\frac{d}{d x} (x sin^{2} (2 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin^{2} (2 x)

= \frac{d x}{d x} sin^{2} (2 x) + \frac{d}{d x} (sin^{2} (2 x)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (sin^{2} (2 x)) = 2 sin (4 x)

= 1 \cdot sin^{2} (2 x) + 2 sin (4 x) x

Simplify

= sin^{2} (2 x) + 2 x sin (4 x)

Popular Examples

derivative of 7^{x^4+2}

\frac{d}{d x} (7^{x^{4} + 2})

derivative of ln(ln(9x))

\frac{d}{d x} (ln (ln (9 x)))

integral from 0 to 9 of 2piy(3-y/3)

\int_{0}^{9} 2 π y (3 - \frac{y}{3}) d y

derivative of-(5e^{5/x}/(x^2))

\frac{d}{d x} (- \frac{5 e ^{\frac{5}{x}}}{x ^{2}})

(\partial)/(\partial x)(30-(x^2+y^2))

\frac{\partial}{\partial x} (30 - (x^{2} + y^{2}))

Frequently Asked Questions (FAQ)

What is the derivative of xsin^2(2x) ?
The derivative of xsin^2(2x) is sin^2(2x)+2xsin(4x)
What is the first derivative of xsin^2(2x) ?
The first derivative of xsin^2(2x) is sin^2(2x)+2xsin(4x)