What is the derivative of f(x)=cos(x^2)2x ?

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

What is the first derivative of f(x)=cos(x^2)2x ?

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

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derivative of

f (x) = cos (x^{2}) 2 x

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int 8 x^{- 1} d x

\int \frac{1}{x ^{2} + 8} d x

f (x) = - 2 x^{3}

\frac{s - 1}{2 s ^{2} + s + 6}

\int_{2}^{4} (2 x^{2} - 3 x + 1) d x

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