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Popular >

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

Solution

derivative of

f (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

integral from 0 to 1/6 of 3/(sqrt(1-9x^2))

\int_{0}^{\frac{1}{6}} \frac{3}{1 - 9 x ^{2}} d x

\frac{d x}{d t} = x t

y^{''}-2y^'+1y=0,y(0)=8,y^'(0)=2

y^{^{''}} - 2 y^{^{'}} + 1 y = 0, y (0) = 8, y^{^{'}} (0) = 2

(\partial)/(\partial y)(-2e^xcos(yz))

\frac{\partial}{\partial y} (- 2 e^{x} cos (yz))

integral of (1/(sqrt(2x)))

\int (\frac{1}{2 x}) d x

Frequently Asked Questions (FAQ)

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