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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

integral of sin^2(xco)s^3x

\int sin^{2} (x co) s^{3} x d x

(\partial)/(\partial y)(5xsin(y))

\frac{\partial}{\partial y} (5 x sin (y))

inverse oflaplace 3x^2 inverse laplace

3 x^{2}

integral of x^{-3}

\int x^{- 3} d x

(\partial)/(\partial x)(x^7yz^2+6yz)

\frac{\partial}{\partial x} (x^{7} y z^{2} + 6 yz)

Frequently Asked Questions (FAQ)

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