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Popular >

d/(dt)(6cos^3(t))

Solution

\frac{d}{d t} (6 cos^{3} (t))

Solution

- 18 cos^{2} (t) sin (t)

Solution steps

\frac{d}{d t} (6 cos^{3} (t))

Take the constant out:

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

= 6 \frac{d}{d t} (cos^{3} (t))

Apply the chain rule:

3 (cos (t))^{2} \frac{d}{d t} (cos (t))

= 3 (cos (t))^{2} \frac{d}{d t} (cos (t))

\frac{d}{d t} (cos (t)) = - sin (t)

= 6 \cdot 3 (cos (t))^{2} (- sin (t))

Simplify

= - 18 cos^{2} (t) sin (t)

Popular Examples

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\int \frac{( 3 x ^{3} - 5 x ^{2} + 10 x - 3 )}{3 x + 1} d x

simplify 8/(sqrt((x^3+x^2+1)^3))simplify

\frac{8}{( x ^{3} + x ^{2} + 1 ) ^{3}}

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\int t - 1 d t

integral of (sin(x))/(sqrt(5cos(x)+10))

\int \frac{sin ( x )}{5 cos ( x ) + 10} d x

(\partial)/(\partial x)(x/(x-y))

\frac{\partial}{\partial x} (\frac{x}{x - y})

Frequently Asked Questions (FAQ)

What is the d/(dt)(6cos^3(t)) ?
The d/(dt)(6cos^3(t)) is -18cos^2(t)sin(t)
What is the first d/(dt)(6cos^3(t)) ?
The first d/(dt)(6cos^3(t)) is -18cos^2(t)sin(t)