What is the derivative of 6sin^5(x)cos(x) ?

The derivative of 6sin^5(x)cos(x) is 6(5sin^4(x)cos^2(x)-sin^6(x))

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

The first derivative of 6sin^5(x)cos(x) is 6(5sin^4(x)cos^2(x)-sin^6(x))

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derivative of

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

6 (5 sin^{4} (x) cos^{2} (x) - sin^{6} (x))

Solution steps

\frac{d}{d x} (6 sin^{5} (x) cos (x))

Take the constant out:

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

= 6 \frac{d}{d x} (sin^{5} (x) cos (x))

Apply the Product Rule:

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

f = sin^{5} (x), g = cos (x)

= 6 (\frac{d}{d x} (sin^{5} (x)) cos (x) + \frac{d}{d x} (cos (x)) sin^{5} (x))

\frac{d}{d x} (sin^{5} (x)) = 5 sin^{4} (x) cos (x)

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

= 6 (5 sin^{4} (x) cos (x) cos (x) + (- sin (x)) sin^{5} (x))

Simplify

6 (5 sin^{4} (x) cos (x) cos (x) + (- sin (x)) sin^{5} (x)) : 6 (5 sin^{4} (x) cos^{2} (x) - sin^{6} (x))

= 6 (5 sin^{4} (x) cos^{2} (x) - sin^{6} (x))

What is the derivative of 6sin^5(x)cos(x) ?
The derivative of 6sin^5(x)cos(x) is 6(5sin^4(x)cos^2(x)-sin^6(x))
What is the first derivative of 6sin^5(x)cos(x) ?
The first derivative of 6sin^5(x)cos(x) is 6(5sin^4(x)cos^2(x)-sin^6(x))