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Popular >

derivative of 3sin^2(2x)

Solution

\frac{d}{d x} (3 sin^{2} (2 x))

Solution

12 sin (2 x) cos (2 x)

Solution steps

\frac{d}{d x} (3 sin^{2} (2 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (sin^{2} (2 x))

Apply the chain rule:

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

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

= 3 \cdot 2 sin (2 x) cos (2 x) \cdot 2

Simplify

= 12 sin (2 x) cos (2 x)

Popular Examples

integral of (sin^2(x))/(1+cos^2(x))

\int \frac{sin ^{2} ( x )}{1 + cos ^{2} ( x )} d x

integral of 15x^3e^x

\int 15 x^{3} e^{x} d x

limit as x approaches infinity of-x

x \to \infty lim (- x)

derivative of 8xarcsin(x)

\frac{d}{d x} (8 x arcsin (x))

derivative of 3xln(9x^2)

\frac{d}{d x} (3 x ln (9 x^{2}))

Frequently Asked Questions (FAQ)

What is the derivative of 3sin^2(2x) ?
The derivative of 3sin^2(2x) is 12sin(2x)cos(2x)
What is the first derivative of 3sin^2(2x) ?
The first derivative of 3sin^2(2x) is 12sin(2x)cos(2x)