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Popular >

derivative of 3sin(xcos^2(x)+sin^3(x))

Solution

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

Solution

3 (- 2 cos (x) + 3 cos^{3} (x)) + 3 sin^{2} (x) cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

(2xy^2+2y)dx+(2x^2y+2x)dy=0

(2 x y^{2} + 2 y) d x + (2 x^{2} y + 2 x) d y = 0

(\partial)/(\partial x)(100e^{(-x-2y)})

\frac{\partial}{\partial x} (100 e^{(- x - 2 y)})

limit as x approaches 1 of g(x)(f(x))

x \to 1 lim (g (x) (f (x)))

limit as x approaches 4 of ((3x^2-17x+20))/(4x^2-25x+36)

x \to 4 lim (\frac{( 3 x ^{2} - 17 x + 20 )}{4 x ^{2} - 25 x + 36})

integral of (ln(cos(x)))/(cos^2(x))

\int \frac{ln ( cos ( x ) )}{cos ^{2} ( x )} d x

Frequently Asked Questions (FAQ)

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