What is the derivative of sin(x^3+sin^3(x)) ?

The derivative of sin(x^3+sin^3(x)) is cos(x^3)*3x^2+3sin^2(x)cos(x)

What is the first derivative of sin(x^3+sin^3(x)) ?

The first derivative of sin(x^3+sin^3(x)) is cos(x^3)*3x^2+3sin^2(x)cos(x)

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\frac{d}{d x} (sin (x^{3}) + sin^{3} (x))

cos (x^{3}) \cdot 3 x^{2} + 3 sin^{2} (x) cos (x)

Solution steps

\frac{d}{d x} (sin (x^{3}) + sin^{3} (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sin (x^{3})) + \frac{d}{d x} (sin^{3} (x))

\frac{d}{d x} (sin (x^{3})) = cos (x^{3}) \cdot 3 x^{2}

\frac{d}{d x} (sin^{3} (x)) = 3 sin^{2} (x) cos (x)

= cos (x^{3}) \cdot 3 x^{2} + 3 sin^{2} (x) cos (x)

What is the derivative of sin(x^3+sin^3(x)) ?
The derivative of sin(x^3+sin^3(x)) is cos(x^3)*3x^2+3sin^2(x)cos(x)
What is the first derivative of sin(x^3+sin^3(x)) ?
The first derivative of sin(x^3+sin^3(x)) is cos(x^3)*3x^2+3sin^2(x)cos(x)