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Popular >

derivative of e^x-e^{xcos(x})

Solution

\frac{d}{d x} (e^{x} - e^{x c o s (x)})

Solution

e^{x} - e^{x c o s (x)} (cos (x) - x sin (x))

Solution steps

\frac{d}{d x} (e^{x} - e^{x c o s (x)})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{x}) - \frac{d}{d x} (e^{x c o s (x)})

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (e^{x c o s (x)}) = e^{x c o s (x)} (cos (x) - x sin (x))

= e^{x} - e^{x c o s (x)} (cos (x) - x sin (x))

Popular Examples

integral from 0 to 3 of 4/(5x^2+6x+1)

\int_{0}^{3} \frac{4}{5 x ^{2} + 6 x + 1} d x

integral from 0 to 1 of (x^3)/(x^4-1)

\int_{0}^{1} \frac{x ^{3}}{x ^{4} - 1} d x

derivative of 9x+2

\frac{d}{d x} (9 x + 2)

y(1-t)dt+t^2(1-t)dy=0

y (1 - t) d t + t^{2} (1 - t) d y = 0

derivative of-(2x/((x^2+1)^2))

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

Frequently Asked Questions (FAQ)

What is the derivative of e^x-e^{xcos(x}) ?
The derivative of e^x-e^{xcos(x}) is e^x-e^{xcos(x)}(cos(x)-xsin(x))
What is the first derivative of e^x-e^{xcos(x}) ?
The first derivative of e^x-e^{xcos(x}) is e^x-e^{xcos(x)}(cos(x)-xsin(x))