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Popular Calculus >

derivative of (1+sin(3x)^4)

Solution

\frac{d}{d x} ((1 + sin (3 x))^{4})

Solution

12 cos (3 x) (1 + sin (3 x))^{3}

Solution steps

\frac{d}{d x} ((1 + sin (3 x))^{4})

Apply the chain rule:

4 (1 + sin (3 x))^{3} \frac{d}{d x} (1 + sin (3 x))

= 4 (1 + sin (3 x))^{3} \frac{d}{d x} (1 + sin (3 x))

\frac{d}{d x} (1 + sin (3 x)) = 3 cos (3 x)

= 4 (1 + sin (3 x))^{3} \cdot 3 cos (3 x)

Simplify

= 12 cos (3 x) (1 + sin (3 x))^{3}

Graph

Popular Examples

derivative of (3cos(2x+sin(3x)+4)^2)

\frac{d}{d x} ((3 cos (2 x) + sin (3 x) + 4)^{2})

y^'-4y=10sin(2t),y(0)=0

y^{^{'}} - 4 y = 10 sin (2 t), y (0) = 0

(\partial)/(\partial y)(ye^{2xy}+x)

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

integral of x/(sqrt(2x^2+3))

\int \frac{x}{2 x ^{2} + 3} d x

derivative of e^x-2e^{-2x}

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

Frequently Asked Questions (FAQ)

What is the derivative of (1+sin(3x)^4) ?
The derivative of (1+sin(3x)^4) is 12cos(3x)(1+sin(3x))^3
What is the first derivative of (1+sin(3x)^4) ?
The first derivative of (1+sin(3x)^4) is 12cos(3x)(1+sin(3x))^3