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Popular >

derivative of axsin(x)

Solution

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

Solution

a (sin (x) + x cos (x))

Solution steps

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

Take the constant out:

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

= a \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)

= a (\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)

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

Simplify

= a (sin (x) + x cos (x))

Popular Examples

(dy)/(dx)=xsqrt(y)cos(x)

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

((dy)/(dt))-(3/t)*y=2t^3e^{2t},y(1)=0

(\frac{d y}{d t}) - (\frac{3}{t}) \cdot y = 2 t^{3} e^{2 t}, y (1) = 0

derivative of f(x)=7x^2+6x derivative of

f (x) = 7 x^{2} + 6 x

tangent of-2x^2,\at x=-2 tangent of

- 2 x^{2}, at x = - 2

tangent of 1/(x^2)tangent of

\frac{1}{x ^{2}}

Frequently Asked Questions (FAQ)

What is the derivative of axsin(x) ?
The derivative of axsin(x) is a(sin(x)+xcos(x))
What is the first derivative of axsin(x) ?
The first derivative of axsin(x) is a(sin(x)+xcos(x))