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

The derivative of 5xsin(x^2) is 5(sin(x^2)+2x^2cos(x^2))

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

The first derivative of 5xsin(x^2) is 5(sin(x^2)+2x^2cos(x^2))

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derivative of

5 x sin (x^{2})

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int \frac{e ^{x}}{x} d x

d er i v a t i v e f (x) = 8 x e^{x} - 8 e^{x}

\frac{d}{d x} (x 4^{x})

d er i v a t i v e x^{13}

im pl i c i t \frac{d y}{d x}, (7 x y + 3)^{2} = 14 y

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