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Popular >

(-sin^3(x)+2cos^2(x)sin(x))^'

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

(sin^{3} (x))^{'} = 3 sin^{2} (x) cos (x)

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

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

Popular Examples

derivative of f(x)= 7/4 x^2-3x+12 derivative of

f (x) = \frac{7}{4} x^{2} - 3 x + 12

derivative of 5sin(10x)

\frac{d}{d x} (5 sin (10 x))

tangent of f(x)=x+sqrt(x),\at x=25 tangent of

f (x) = x + x, at x = 25

derivative of y=x^{-9}derivative of

y = x^{- 9}

derivative of 10sin^3(x)

\frac{d}{d x} (10 sin^{3} (x))

Frequently Asked Questions (FAQ)

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