What is the derivative of 3sin^4(x) ?

The derivative of 3sin^4(x) is 12sin^3(x)cos(x)

What is the first derivative of 3sin^4(x) ?

The first derivative of 3sin^4(x) is 12sin^3(x)cos(x)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

\frac{d ^{2} x}{d t ^{2}} + a x = 0

\frac{d}{d x} (1 - 2 x + 3 x^{2} - 4 x^{3})

\int e^{0.2 x} d x

y^{^{''}} - 9 y^{^{'}} = 81 t, y (0) = 9, y^{^{'}} (0) = 0

\int \frac{- 3}{7 e ^{7 x}} d x

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