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

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

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

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

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

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

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

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

g (x) = - x^{5} + 4 x^{2} - 2 x + 2

\int \frac{sin ( 2 x )}{18 + cos ^{2} ( x )} d x

\frac{d}{d x} (\frac{4 x ^{5} - 5 x ^{4} + 6 x - 2}{x ^{4}})

y^{^{'}} + 3 y + 5 = 0

\frac{d}{d x} (3 x^{2} + 12 x + 6)

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