What is the derivative of x^5-e^xln(x) ?

The derivative of x^5-e^xln(x) is 5x^4-e^xln(x)-(e^x)/x

What is the first derivative of x^5-e^xln(x) ?

The first derivative of x^5-e^xln(x) is 5x^4-e^xln(x)-(e^x)/x

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\frac{d}{d x} (x^{5} - e^{x} ln (x))

5 x^{4} - e^{x} ln (x) - \frac{e ^{x}}{x}

Solution steps

\frac{d}{d x} (x^{5} - e^{x} ln (x))

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= 5 x^{4} - e^{x} ln (x) - \frac{e ^{x}}{x}

x \to - \infty lim (5 x)

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What is the derivative of x^5-e^xln(x) ?
The derivative of x^5-e^xln(x) is 5x^4-e^xln(x)-(e^x)/x
What is the first derivative of x^5-e^xln(x) ?
The first derivative of x^5-e^xln(x) is 5x^4-e^xln(x)-(e^x)/x