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)

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

- 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})

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)