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

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

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

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

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derivative of

- sin (x^{2}) (2 x)

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int 2 e^{3 t} d t

\int_{0}^{3} 1 + 4 x^{2} d x

f (x) = 2 x^{3} - 6 x^{2} - 90 x - 1

\frac{d}{d t} (a t^{2} + b t + c)

\int \frac{1}{50} d x

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