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Popular >

derivative of cos^3(x+sin^4(x))

Solution

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

Solution

- 3 cos^{2} (x) sin (x) + 4 sin^{3} (x) cos (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= - 3 cos^{2} (x) sin (x) + 4 sin^{3} (x) cos (x)

Popular Examples

(\partial)/(\partial x)(8ln(cos(x)))

\frac{\partial}{\partial x} (8 ln (cos (x)))

(\partial)/(\partial x)(5sin(3x)cos(4y))

\frac{\partial}{\partial x} (5 sin (3 x) cos (4 y))

y^'=-2y+5t,y(0)=-4

y^{^{'}} = - 2 y + 5 t, y (0) = - 4

integral of e^{9x}cos(8x)

\int e^{9 x} cos (8 x) d x

(\partial)/(\partial z)(2x^{y/z})

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

Frequently Asked Questions (FAQ)

What is the derivative of cos^3(x+sin^4(x)) ?
The derivative of cos^3(x+sin^4(x)) is -3cos^2(x)sin(x)+4sin^3(x)cos(x)
What is the first derivative of cos^3(x+sin^4(x)) ?
The first derivative of cos^3(x+sin^4(x)) is -3cos^2(x)sin(x)+4sin^3(x)cos(x)