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Popular >

derivative of y=x+e^x-1/x

Solution

derivative of

y = x + e^{x} - \frac{1}{x}

Solution

1 + e^{x} + \frac{1}{x ^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d x}{d x} = 1

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

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

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

Simplify

= 1 + e^{x} + \frac{1}{x ^{2}}

Popular Examples

derivative of (cos(x))/(2+sin(x))derivative of

\frac{cos ( x )}{2 + sin ( x )}

limit as x approaches 0 of (9sin(x))/x

x \to 0 lim (\frac{9 sin ( x )}{x})

integral of (sqrt(x))/(x-25)

\int \frac{x}{x - 25} d x

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\int 3 t t^{2} + 8 d t

(\partial)/(\partial x)(cos^6(y^7x^8))

\frac{\partial}{\partial x} (cos^{6} (y^{7} x^{8}))

Frequently Asked Questions (FAQ)

What is the derivative of y=x+e^x-1/x ?
The derivative of y=x+e^x-1/x is 1+e^x+1/(x^2)
What is the first derivative of y=x+e^x-1/x ?
The first derivative of y=x+e^x-1/x is 1+e^x+1/(x^2)