What is the derivative of 4t^3cos(t) ?

The derivative of 4t^3cos(t) is 4(3t^2cos(t)-t^3sin(t))

What is the first derivative of 4t^3cos(t) ?

The first derivative of 4t^3cos(t) is 4(3t^2cos(t)-t^3sin(t))

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derivative of

4 t^{3} cos (t)

4 (3 t^{2} cos (t) - t^{3} sin (t))

Solution steps

\frac{d}{d t} (4 t^{3} cos (t))

Take the constant out:

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

= 4 \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)

= 4 (\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)

= 4 (3 t^{2} cos (t) + (- sin (t)) t^{3})

Simplify

= 4 (3 t^{2} cos (t) - t^{3} sin (t))

\int_{- \infty}^{12} r e^{\frac{r}{3}} d r

\frac{\partial}{\partial t} (x y z^{2} tan (y t))

x^{2} + x y - y^{2} = - 9, (3, 6)

\frac{2 x}{1 + x ^{2}}

F (x) = ln (2 x), y = 0, y = 2

What is the derivative of 4t^3cos(t) ?
The derivative of 4t^3cos(t) is 4(3t^2cos(t)-t^3sin(t))
What is the first derivative of 4t^3cos(t) ?
The first derivative of 4t^3cos(t) is 4(3t^2cos(t)-t^3sin(t))