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Popular >

derivative of 5xsin(x)

Solution

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

Solution

5 (sin (x) + x cos (x))

Solution steps

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

Take the constant out:

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

= 5 \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)

= 5 (\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)

= 5 (1 \cdot sin (x) + cos (x) x)

Simplify

= 5 (sin (x) + x cos (x))

Popular Examples

derivative of \sqrt[3]{x-2}derivative of

derivative of 3x^2-2x+4

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

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

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

limit as x approaches 1 of (2x+3)/(x+1)

x \to 1 lim (\frac{2 x + 3}{x + 1})

(\partial}{\partial y}(166x+456y-\frac{5000)/x-(1080)/y+43590)

\frac{\partial}{\partial y} (166 x + 456 y - \frac{5000}{x} - \frac{1080}{y} + 43590)

Frequently Asked Questions (FAQ)

What is the derivative of 5xsin(x) ?
The derivative of 5xsin(x) is 5(sin(x)+xcos(x))
What is the first derivative of 5xsin(x) ?
The first derivative of 5xsin(x) is 5(sin(x)+xcos(x))