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Popular >

derivative of x*sin(x^2)

Solution

derivative of

x \cdot sin (x^{2})

Solution

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

Solution steps

\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})

= \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

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

Simplify

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

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

Popular Examples

tangent of x^2+xy-y^2=19,(4,1)tangent of

x^{2} + x y - y^{2} = 19, (4, 1)

limit as x approaches 0+of (cos(x)-1)/x

x \to 0 + lim (\frac{cos ( x ) - 1}{x})

integral from-3 to 3 of sqrt(1+(x)^2)

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

derivative of x^2-4x+8 derivative of

x^{2} - 4 x + 8

inverse oflaplace (s+1)/(s^2+3s)inverse laplace

\frac{s + 1}{s ^{2} + 3 s}

Frequently Asked Questions (FAQ)

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