What is the derivative of x^8cos(x) ?

The derivative of x^8cos(x) is 8x^7cos(x)-x^8sin(x)

What is the first derivative of x^8cos(x) ?

The first derivative of x^8cos(x) is 8x^7cos(x)-x^8sin(x)

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\frac{d}{d x} (x^{8} cos (x))

8 x^{7} cos (x) - x^{8} sin (x)

Solution steps

\frac{d}{d x} (x^{8} cos (x))

Apply the Product Rule:

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

f = x^{8}, g = cos (x)

= \frac{d}{d x} (x^{8}) cos (x) + \frac{d}{d x} (cos (x)) x^{8}

\frac{d}{d x} (x^{8}) = 8 x^{7}

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

= 8 x^{7} cos (x) + (- sin (x)) x^{8}

Simplify

= 8 x^{7} cos (x) - x^{8} sin (x)

\frac{\partial}{\partial y} (y^{4} + 5 x y^{3})

\int (54) d x

\int \frac{9 x ^{2}}{1 - x ^{3}} d x

y = x^{2} - 1, y = 0, [0, 3]

f (x) = \frac{1}{4} x - \frac{1}{6}

What is the derivative of x^8cos(x) ?
The derivative of x^8cos(x) is 8x^7cos(x)-x^8sin(x)
What is the first derivative of x^8cos(x) ?
The first derivative of x^8cos(x) is 8x^7cos(x)-x^8sin(x)