What is the derivative of 9x^{ln(9x)} ?

The derivative of 9x^{ln(9x)} is 3^{2+2ln(x)}x^{ln(x)-1}ln(9x^2)

What is the first derivative of 9x^{ln(9x)} ?

The first derivative of 9x^{ln(9x)} is 3^{2+2ln(x)}x^{ln(x)-1}ln(9x^2)

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derivative of

9 x^{l n (9 x)}

3^{2 + 2 l n (x)} x^{l n (x) - 1} ln (9 x^{2})

Solution steps

\frac{d}{d x} (9 x^{l n (9 x)})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 9 \frac{d}{d x} (x^{l n (9 x)})

Apply exponent rule:

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

x^{l n (9 x)} = e^{l n (9 x) l n (x)}

= 9 \frac{d}{d x} (e^{l n (9 x) l n (x)})

Apply the chain rule:

e^{l n (9 x) l n (x)} \frac{d}{d x} (ln (9 x) ln (x))

= e^{l n (9 x) l n (x)} \frac{d}{d x} (ln (9 x) ln (x))

\frac{d}{d x} (ln (9 x) ln (x)) = \frac{ln ( 9 x ^{2} )}{x}

= 9 e^{l n (9 x) l n (x)} \frac{ln ( 9 x ^{2} )}{x}

Simplify

9 e^{l n (9 x) l n (x)} \frac{ln ( 9 x ^{2} )}{x} : 3^{2 + 2 l n (x)} x^{l n (x) - 1} ln (9 x^{2})

= 3^{2 + 2 l n (x)} x^{l n (x) - 1} ln (9 x^{2})

h (x) = e^{x} + x^{5}

x \to \frac{5}{2} lim (x^{2} + 2 x + 4)

\int cos (\frac{3 x}{2}) d x

x \to - 3 lim (\frac{1}{x - 3})

\frac{d}{d x} (2 (x^{^{'}} - n) e^{- (p (x, t) t)})

What is the derivative of 9x^{ln(9x)} ?
The derivative of 9x^{ln(9x)} is 3^{2+2ln(x)}x^{ln(x)-1}ln(9x^2)
What is the first derivative of 9x^{ln(9x)} ?
The first derivative of 9x^{ln(9x)} is 3^{2+2ln(x)}x^{ln(x)-1}ln(9x^2)