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Popular >

derivative of sin(x^3+sin^3(x))

Solution

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

Solution

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)

Popular Examples

integral from-4 to 1 of (3x+6)

\int_{- 4}^{1} (3 x + 6) d x

derivative of (arctan(x)^3)

\frac{d}{d x} ((arctan (x))^{3})

(\partial)/(\partial x)(1/(f(x))-1/x)

\frac{\partial}{\partial x} (\frac{1}{f ( x )} - \frac{1}{x})

(\partial)/(\partial z)((x+y)/(z-2y))

\frac{\partial}{\partial z} (\frac{x + y}{z - 2 y})

derivative of sqrt(y^2+x^2)

\frac{d}{d x} (y^{2} + x^{2})

Frequently Asked Questions (FAQ)

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)