What is the derivative of (x^{18})^x ?

The derivative of (x^{18})^x is e^{xln(x^{18})}(ln(x^{18})+18)

What is the first derivative of (x^{18})^x ?

The first derivative of (x^{18})^x is e^{xln(x^{18})}(ln(x^{18})+18)

Popular >

derivative of

(x^{18})^{x}

e^{x l n (x^{18})} (ln (x^{18}) + 18)

Solution steps

\frac{d}{d x} ((x^{18})^{x})

Apply exponent rule:

a^{b} = e^{b l n (a)}

(x^{18})^{x} = e^{x l n (x^{18})}

= \frac{d}{d x} (e^{x l n (x^{18})})

Apply the chain rule:

e^{x l n (x^{18})} \frac{d}{d x} (x ln (x^{18}))

= e^{x l n (x^{18})} \frac{d}{d x} (x ln (x^{18}))

\frac{d}{d x} (x ln (x^{18})) = ln (x^{18}) + 18

= e^{x l n (x^{18})} (ln (x^{18}) + 18)

\frac{d}{d z} (\frac{( 3 z + 2 i )}{( 4 z - 5 i )})

lo g_{10} ((x + 1)^{x + 1})

x^{2} + 2 x - 18

x (lo g_{10} (∣ x ∣) - 1)

y = \frac{2 sin ( x )}{5}

What is the derivative of (x^{18})^x ?
The derivative of (x^{18})^x is e^{xln(x^{18})}(ln(x^{18})+18)
What is the first derivative of (x^{18})^x ?
The first derivative of (x^{18})^x is e^{xln(x^{18})}(ln(x^{18})+18)