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Popular >

derivative of xcos(x^2+1-ln(3-x))

Solution

\frac{d}{d x} (x cos (x^{2} + 1) - ln (3 - x))

Solution

cos (x^{2} + 1) - 2 x^{2} sin (x^{2} + 1) + \frac{1}{3 - x}

Solution steps

\frac{d}{d x} (x cos (x^{2} + 1) - ln (3 - x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x cos (x^{2} + 1)) - \frac{d}{d x} (ln (3 - x))

\frac{d}{d x} (x cos (x^{2} + 1)) = cos (x^{2} + 1) - 2 x^{2} sin (x^{2} + 1)

\frac{d}{d x} (ln (3 - x)) = - \frac{1}{3 - x}

= cos (x^{2} + 1) - 2 x^{2} sin (x^{2} + 1) - (- \frac{1}{3 - x})

Simplify

= cos (x^{2} + 1) - 2 x^{2} sin (x^{2} + 1) + \frac{1}{3 - x}

Popular Examples

integral of (2arctan(n))/(1+n^2)

\int \frac{2 arctan ( n )}{1 + n ^{2}} d n

integral from 6 to 7 of x/(x^2+4x+20)

\int_{6}^{7} \frac{x}{x ^{2} + 4 x + 20} d x

integral of (x^3)/(sqrt(x^2+\sqrt{2))}

\int \frac{x ^{3}}{x ^{2} + 2} d x

integral of (cos(ax))/(1-sin(ax))

\int \frac{cos ( a x )}{1 - sin ( a x )} d x

sum from n=1 to infinity of (x^n)/(4n-1)

n = 1 \sum \infty \frac{x ^{n}}{4 n - 1}

Frequently Asked Questions (FAQ)

What is the derivative of xcos(x^2+1-ln(3-x)) ?
The derivative of xcos(x^2+1-ln(3-x)) is cos(x^2+1)-2x^2sin(x^2+1)+1/(3-x)
What is the first derivative of xcos(x^2+1-ln(3-x)) ?
The first derivative of xcos(x^2+1-ln(3-x)) is cos(x^2+1)-2x^2sin(x^2+1)+1/(3-x)