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

The derivative of-sin(x^2+3*2x) is -2(2x^2cos(x^2+3)+sin(x^2+3))

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

The first derivative of-sin(x^2+3*2x) is -2(2x^2cos(x^2+3)+sin(x^2+3))

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x^{2} + 3), g = x

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

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

\frac{d x}{d x} = 1

= - 2 (cos (x^{2} + 3) \cdot 2 xx + 1 \cdot sin (x^{2} + 3))

Simplify

- 2 (cos (x^{2} + 3) \cdot 2 xx + 1 \cdot sin (x^{2} + 3)) : - 2 (2 x^{2} cos (x^{2} + 3) + sin (x^{2} + 3))

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

\int 5 x^{2} (2 x^{3} + 3)^{4} d x

\int \frac{( ln ( ln ( x ) ) )}{x} d x

\frac{\partial}{\partial y} (y e^{- x})

x \to - 2 lim (x^{2} + 5 x + 7)

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