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Popular >

derivative of g(t)=t^3cos(t)

Solution

derivative of

g (t) = t^{3} cos (t)

Solution

3 t^{2} cos (t) - t^{3} sin (t)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t^{3}, g = cos (t)

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

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

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

= 3 t^{2} cos (t) + (- sin (t)) t^{3}

Simplify

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

Popular Examples

derivative of ln(2x^2-1)

\frac{d}{d x} (ln (2 x^{2} - 1))

limit as x approaches-0.00000001 of x^x

x \to - 0.00000001 lim (x^{x})

derivative of f(x)=[x+(x+sin^2(x))^3]^4 derivative of

f (x) = [x + (x + sin^{2} (x))^{3}]^{4}

derivative of f(x)=x^2+5-3x^{-2}derivative of

f (x) = x^{2} + 5 - 3 x^{- 2}

limit as x approaches infinity of ((13x)/(13x+3))^{5x}

x \to \infty lim ((\frac{13 x}{13 x + 3})^{5 x})

Frequently Asked Questions (FAQ)

What is the derivative of g(t)=t^3cos(t) ?
The derivative of g(t)=t^3cos(t) is 3t^2cos(t)-t^3sin(t)
What is the first derivative of g(t)=t^3cos(t) ?
The first derivative of g(t)=t^3cos(t) is 3t^2cos(t)-t^3sin(t)