What is the derivative of (x^5+e^x)/(x+2) ?

The derivative of (x^5+e^x)/(x+2) is (4x^5+10x^4+e^xx+e^x)/((x+2)^2)

What is the first derivative of (x^5+e^x)/(x+2) ?

The first derivative of (x^5+e^x)/(x+2) is (4x^5+10x^4+e^xx+e^x)/((x+2)^2)

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derivative of

\frac{x ^{5} + e ^{x}}{x + 2}

\frac{4 x ^{5} + 10 x ^{4} + e ^{x} x + e ^{x}}{( x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{5} + e ^{x}}{x + 2})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{5} + e ^{x} ) ( x + 2 ) - \frac{d}{d x} ( x + 2 ) ( x ^{5} + e ^{x} )}{( x + 2 ) ^{2}}

\frac{d}{d x} (x^{5} + e^{x}) = 5 x^{4} + e^{x}

\frac{d}{d x} (x + 2) = 1

= \frac{( 5 x ^{4} + e ^{x} ) ( x + 2 ) - 1 \cdot ( x ^{5} + e ^{x} )}{( x + 2 ) ^{2}}

Simplify

\frac{( 5 x ^{4} + e ^{x} ) ( x + 2 ) - 1 \cdot ( x ^{5} + e ^{x} )}{( x + 2 ) ^{2}} : \frac{4 x ^{5} + 10 x ^{4} + e ^{x} x + e ^{x}}{( x + 2 ) ^{2}}

= \frac{4 x ^{5} + 10 x ^{4} + e ^{x} x + e ^{x}}{( x + 2 ) ^{2}}

What is the derivative of (x^5+e^x)/(x+2) ?
The derivative of (x^5+e^x)/(x+2) is (4x^5+10x^4+e^xx+e^x)/((x+2)^2)
What is the first derivative of (x^5+e^x)/(x+2) ?
The first derivative of (x^5+e^x)/(x+2) is (4x^5+10x^4+e^xx+e^x)/((x+2)^2)