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

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

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}

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

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

f (x) = - \frac{3}{e ^{3 x}}

x \to - 3 lim (x^{2} + 4 x + 1)

\int \frac{1}{x ( 4 - x )} d x

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