What is the derivative of 5xcos(x^2) ?

The derivative of 5xcos(x^2) is 5(cos(x^2)-2x^2sin(x^2))

What is the first derivative of 5xcos(x^2) ?

The first derivative of 5xcos(x^2) is 5(cos(x^2)-2x^2sin(x^2))

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\frac{d}{d x} (5 x cos (x^{2}))

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

Solution steps

\frac{d}{d x} (5 x cos (x^{2}))

Take the constant out:

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

= 5 \frac{d}{d x} (x cos (x^{2}))

Apply the Product Rule:

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

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

= 5 (\frac{d x}{d x} cos (x^{2}) + \frac{d}{d x} (cos (x^{2})) x)

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

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

= 5 (1 \cdot cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) x)

Simplify

5 (1 \cdot cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) x) : 5 (cos (x^{2}) - 2 x^{2} sin (x^{2}))

= 5 (cos (x^{2}) - 2 x^{2} sin (x^{2}))

x \to + 0 lim (\frac{5}{x ^{2} + x} - \frac{5}{x})

ln (\frac{x - 1}{x + 1})

x \to 3 lim (\frac{sin ( x )}{x})

\int \frac{72}{1 - cos ( 9 x )} d x

\frac{d}{d x} (x^{2} - y)

What is the derivative of 5xcos(x^2) ?
The derivative of 5xcos(x^2) is 5(cos(x^2)-2x^2sin(x^2))
What is the first derivative of 5xcos(x^2) ?
The first derivative of 5xcos(x^2) is 5(cos(x^2)-2x^2sin(x^2))