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

The derivative of sin(3x-4x^4+2x^3+3) is -16x^3+6x^2+3cos(3x)

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

The first derivative of sin(3x-4x^4+2x^3+3) is -16x^3+6x^2+3cos(3x)

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\frac{d}{d x} (sin (3 x) - 4 x^{4} + 2 x^{3} + 3)

- 16 x^{3} + 6 x^{2} + 3 cos (3 x)

Solution steps

\frac{d}{d x} (sin (3 x) - 4 x^{4} + 2 x^{3} + 3)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sin (3 x)) - \frac{d}{d x} (4 x^{4}) + \frac{d}{d x} (2 x^{3}) + \frac{d}{d x} (3)

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

\frac{d}{d x} (4 x^{4}) = 16 x^{3}

\frac{d}{d x} (2 x^{3}) = 6 x^{2}

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

= cos (3 x) \cdot 3 - 16 x^{3} + 6 x^{2} + 0

Simplify

= - 16 x^{3} + 6 x^{2} + 3 cos (3 x)

\int 7 e^{- 7 x} sin (7 x) d x

\frac{d y}{d x} = \frac{2 y}{x} + x^{2} y^{5}

\int_{0}^{1} 4 e^{5 x} d x

\int 2 - 4 x d x

\frac{d ^{2}}{d x ^{2}} (e^{9 e^{x}})

What is the derivative of sin(3x-4x^4+2x^3+3) ?
The derivative of sin(3x-4x^4+2x^3+3) is -16x^3+6x^2+3cos(3x)
What is the first derivative of sin(3x-4x^4+2x^3+3) ?
The first derivative of sin(3x-4x^4+2x^3+3) is -16x^3+6x^2+3cos(3x)