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Popular >

d/(dt)(3t^2-5cos^3(t))

Solution

\frac{d}{d t} (3 t^{2} - 5 cos^{3} (t))

Solution

6 t + 15 cos^{2} (t) sin (t)

Solution steps

\frac{d}{d t} (3 t^{2} - 5 cos^{3} (t))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (3 t^{2}) - \frac{d}{d t} (5 cos^{3} (t))

\frac{d}{d t} (3 t^{2}) = 6 t

\frac{d}{d t} (5 cos^{3} (t)) = - 15 cos^{2} (t) sin (t)

= 6 t - (- 15 cos^{2} (t) sin (t))

Simplify

= 6 t + 15 cos^{2} (t) sin (t)

Graph

Popular Examples

derivative of 2cos(3x+2sin(10y)+3x-10y)

\frac{d}{d x} (2 cos (3 x) + 2 sin (10 y) + 3 x - 10 y)

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\frac{x ^{3} + 8}{3}

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d/(da)(sec^2(a)+cos^2(a))

\frac{d}{d a} (sec^{2} (a) + cos^{2} (a))

Frequently Asked Questions (FAQ)

What is the d/(dt)(3t^2-5cos^3(t)) ?
The d/(dt)(3t^2-5cos^3(t)) is 6t+15cos^2(t)sin(t)
What is the first d/(dt)(3t^2-5cos^3(t)) ?
The first d/(dt)(3t^2-5cos^3(t)) is 6t+15cos^2(t)sin(t)