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

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

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

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

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derivative of

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

cos (x^{6}) \cdot 6 x^{5} + 6 sin^{5} (x) cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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