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Popular >

derivative of f(t)=t^9sin(t)

Solution

derivative of

f (t) = t^{9} sin (t)

Solution

9 t^{8} sin (t) + cos (t) t^{9}

Solution steps

\frac{d}{d t} (t^{9} sin (t))

Apply the Product Rule:

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

f = t^{9}, g = sin (t)

= \frac{d}{d t} (t^{9}) sin (t) + \frac{d}{d t} (sin (t)) t^{9}

\frac{d}{d t} (t^{9}) = 9 t^{8}

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

= 9 t^{8} sin (t) + cos (t) t^{9}

Popular Examples

integral from 1 to e of 4x^3ln(x)

\int_{1}^{e} 4 x^{3} ln (x) d x

derivative of-1/2 x derivative of

- \frac{1}{2} x

(\partial)/(\partial x)(x^3e^x)

\frac{\partial}{\partial x} (x^{3} e^{x})

sum from n=0 to infinity of (9^n)/(n!)

n = 0 \sum \infty \frac{9 ^{n}}{n !}

integral of 3/2 e^{-x}cos(2x)

\int \frac{3}{2} e^{- x} cos (2 x) d x

Frequently Asked Questions (FAQ)

What is the derivative of f(t)=t^9sin(t) ?
The derivative of f(t)=t^9sin(t) is 9t^8sin(t)+cos(t)t^9
What is the first derivative of f(t)=t^9sin(t) ?
The first derivative of f(t)=t^9sin(t) is 9t^8sin(t)+cos(t)t^9