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

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

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

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

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derivative of

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)

\int_{0}^{1} x ln (x + 1) d x

2 \frac{d y}{d x} = \frac{y}{x} - \frac{x}{y ^{2}}

\int_{0}^{10} 1200 t e^{- 0.5 t} d t

\frac{d y}{d x} = x^{2} (2 y - 3)^{2}, y (0) = - 1

\int \frac{tan ( x ) sin ( x )}{1} d x

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