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Popular >

derivative of 10xsin(x)

Solution

\frac{d}{d x} (10 x sin (x))

Solution

10 (sin (x) + x cos (x))

Solution steps

\frac{d}{d x} (10 x sin (x))

Take the constant out:

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

= 10 \frac{d}{d x} (x sin (x))

Apply the Product Rule:

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

f = x, g = sin (x)

= 10 (\frac{d x}{d x} sin (x) + \frac{d}{d x} (sin (x)) x)

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

\frac{d}{d x} (sin (x)) = cos (x)

= 10 (1 \cdot sin (x) + cos (x) x)

Simplify

= 10 (sin (x) + x cos (x))

Popular Examples

9x^2y^2+x^{3/2}y^'=y^2

9 x^{2} y^{2} + x^{\frac{3}{2}} y^{^{'}} = y^{2}

derivative of (x^2-18)(2x+3)derivative of

(x^{2} - 18) (2 x + 3)

integral of x+1/(x^2)

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

(\partial)/(\partial x)(xy-1)

\frac{\partial}{\partial x} (x y - 1)

(\partial)/(\partial y)((x^2-1)(y+2))

\frac{\partial}{\partial y} ((x^{2} - 1) (y + 2))

Frequently Asked Questions (FAQ)

What is the derivative of 10xsin(x) ?
The derivative of 10xsin(x) is 10(sin(x)+xcos(x))
What is the first derivative of 10xsin(x) ?
The first derivative of 10xsin(x) is 10(sin(x)+xcos(x))