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Popular >

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

Solution

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

Solution

- 9 x^{2} sin (x^{3}) - 12 x^{2} cos (x^{3})

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (3) = 0

\frac{d}{d x} (3 cos (x^{3})) = - 9 x^{2} sin (x^{3})

\frac{d}{d x} (4 sin (x^{3})) = 12 x^{2} cos (x^{3})

= 0 - 9 x^{2} sin (x^{3}) - 12 x^{2} cos (x^{3})

Simplify

= - 9 x^{2} sin (x^{3}) - 12 x^{2} cos (x^{3})

Popular Examples

integral from 3 to 5 of ln(x^2+1)

\int_{3}^{5} ln (x^{2} + 1) d x

derivative of arctan(sqrt(x/a))

\frac{d}{d x} (arctan (\frac{x}{a}))

derivative of-1/2 e^{-x/2}

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

integral of (x^2-3x+11)/((x^2-4x+10)^2)

\int \frac{x ^{2} - 3 x + 11}{( x ^{2} - 4 x + 10 ) ^{2}} d x

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

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

Frequently Asked Questions (FAQ)

What is the derivative of 3+3cos(x^3-4sin(x^3)) ?
The derivative of 3+3cos(x^3-4sin(x^3)) is -9x^2sin(x^3)-12x^2cos(x^3)
What is the first derivative of 3+3cos(x^3-4sin(x^3)) ?
The first derivative of 3+3cos(x^3-4sin(x^3)) is -9x^2sin(x^3)-12x^2cos(x^3)