What is the derivative of f(x)=x^9cos(x) ?

The derivative of f(x)=x^9cos(x) is 9x^8cos(x)-x^9sin(x)

What is the first derivative of f(x)=x^9cos(x) ?

The first derivative of f(x)=x^9cos(x) is 9x^8cos(x)-x^9sin(x)

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derivative of

f (x) = x^{9} cos (x)

9 x^{8} cos (x) - x^{9} sin (x)

Solution steps

\frac{d}{d x} (x^{9} cos (x))

Apply the Product Rule:

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

f = x^{9}, g = cos (x)

= \frac{d}{d x} (x^{9}) cos (x) + \frac{d}{d x} (cos (x)) x^{9}

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

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

= 9 x^{8} cos (x) + (- sin (x)) x^{9}

Simplify

= 9 x^{8} cos (x) - x^{9} sin (x)

t^{2} e^{- 3 t}

\frac{d}{d x} (y^{2} x + 2 y x^{3})

(0, - 2), (2, 2)

\int_{0}^{1} x + 16 d x

sin (x + π)

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