What is the derivative of 5x^7sin(x) ?

The derivative of 5x^7sin(x) is 5(7x^6sin(x)+cos(x)x^7)

What is the first derivative of 5x^7sin(x) ?

The first derivative of 5x^7sin(x) is 5(7x^6sin(x)+cos(x)x^7)

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\frac{d}{d x} (5 x^{7} sin (x))

5 (7 x^{6} sin (x) + cos (x) x^{7})

Solution steps

\frac{d}{d x} (5 x^{7} sin (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 5 \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)

= 5 (\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)

= 5 (7 x^{6} sin (x) + cos (x) x^{7})

What is the derivative of 5x^7sin(x) ?
The derivative of 5x^7sin(x) is 5(7x^6sin(x)+cos(x)x^7)
What is the first derivative of 5x^7sin(x) ?
The first derivative of 5x^7sin(x) is 5(7x^6sin(x)+cos(x)x^7)