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Popular >

derivative of a(sin(x-xcos(x)))

Solution

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

Solution

a x sin (x)

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= a (cos (x) - (cos (x) - x sin (x)))

Simplify

= a x sin (x)

Popular Examples

integral of xln(x-2)

\int x ln (x - 2) d x

integral of (e^x)/(1-e^x)

\int \frac{e ^{x}}{1 - e ^{x}} d x

derivative of xsqrt(3)-2x^2

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

integral from 0 to 1 of 4(1+sqrt(x))^7

\int_{0}^{1} 4 (1 + x)^{7} d x

derivative of 800sqrt(x^2-0.1x)

\frac{d}{d x} (800 x^{2} - 0.1 x)

Frequently Asked Questions (FAQ)

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