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Popular >

derivative of e^x(tan(x-x))

Solution

\frac{d}{d x} (e^{x} (tan (x) - x))

Solution

e^{x} (tan (x) - x) + tan^{2} (x) e^{x}

Solution steps

\frac{d}{d x} (e^{x} (tan (x) - x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = tan (x) - x

= \frac{d}{d x} (e^{x}) (tan (x) - x) + \frac{d}{d x} (tan (x) - x) e^{x}

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

\frac{d}{d x} (tan (x) - x) = tan^{2} (x)

= e^{x} (tan (x) - x) + tan^{2} (x) e^{x}

Popular Examples

limit as x approaches 0 of x/(x+1)

x \to 0 lim (\frac{x}{x + 1})

derivative of 2x^3+3x^2-12x+2 derivative of

2 x^{3} + 3 x^{2} - 12 x + 2

integral of (x^2-5x)*e^x

\int (x^{2} - 5 x) \cdot e^{x} d x

tangent of y=10xsin(x),(pi/2 ,5pi)tangent of

y = 10 x sin (x), (\frac{π}{2}, 5 π)

integral of 3arctan(sqrt(x))

\int 3 arctan (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of e^x(tan(x-x)) ?
The derivative of e^x(tan(x-x)) is e^x(tan(x)-x)+tan^2(x)e^x
What is the first derivative of e^x(tan(x-x)) ?
The first derivative of e^x(tan(x-x)) is e^x(tan(x)-x)+tan^2(x)e^x