What is the derivative of x^7cos(x) ?

The derivative of x^7cos(x) is 7x^6cos(x)-x^7sin(x)

What is the first derivative of x^7cos(x) ?

The first derivative of x^7cos(x) is 7x^6cos(x)-x^7sin(x)

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\frac{d}{d x} (x^{7} cos (x))

7 x^{6} cos (x) - x^{7} sin (x)

Solution steps

\frac{d}{d x} (x^{7} cos (x))

Apply the Product Rule:

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

f = x^{7}, g = cos (x)

= \frac{d}{d x} (x^{7}) cos (x) + \frac{d}{d x} (cos (x)) x^{7}

\frac{d}{d x} (x^{7}) = 7 x^{6}

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

= 7 x^{6} cos (x) + (- sin (x)) x^{7}

Simplify

= 7 x^{6} cos (x) - x^{7} sin (x)

\frac{u}{u ^{2} + 6}

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\int x 7^{x} d x

\int \frac{sin ( 2 x )}{4 + cos ^{2} ( x )} d x

What is the derivative of x^7cos(x) ?
The derivative of x^7cos(x) is 7x^6cos(x)-x^7sin(x)
What is the first derivative of x^7cos(x) ?
The first derivative of x^7cos(x) is 7x^6cos(x)-x^7sin(x)