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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 8)^{5})

\frac{1 - ln ( x - 1 )}{( x - 1 ) ^{2}}

\int x^{2} 7 x + 7 d x

\frac{\partial}{\partial y} (x yz - cos (x + y + z))

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