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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

d/(dy)(sqrt(tan(x)+y))

\frac{d}{d y} (tan (x) + y)

derivative of x^{(-1/2})

\frac{d}{d x} (x^{\frac{- 1}{2}})

integral of ((arctan(x))^2)/(x^2+1)

\int \frac{( arctan ( x ) ) ^{2}}{x ^{2} + 1} d x

inverse oflaplace 1/((s-4))inverse laplace

\frac{1}{( s - 4 )}

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\frac{\partial}{\partial y} (x^{2} yz + \frac{1}{x y z ^{2}})

Frequently Asked Questions (FAQ)

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