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Popular Calculus >

derivative of (sin(x)^4+sin(x^4))

Solution

\frac{d}{d x} ((sin (x))^{4} + sin (x^{4}))

Solution

4 sin^{3} (x) cos (x) + cos (x^{4}) \cdot 4 x^{3}

Solution steps

\frac{d}{d x} ((sin (x))^{4} + sin (x^{4}))

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} ((sin (x))^{4}) = 4 sin^{3} (x) cos (x)

\frac{d}{d x} (sin (x^{4})) = cos (x^{4}) \cdot 4 x^{3}

= 4 sin^{3} (x) cos (x) + cos (x^{4}) \cdot 4 x^{3}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (sin(x)^4+sin(x^4)) ?
The derivative of (sin(x)^4+sin(x^4)) is 4sin^3(x)cos(x)+cos(x^4)*4x^3
What is the first derivative of (sin(x)^4+sin(x^4)) ?
The first derivative of (sin(x)^4+sin(x^4)) is 4sin^3(x)cos(x)+cos(x^4)*4x^3