What is the derivative of f(x)=6x^{ln(x)} ?

The derivative of f(x)=6x^{ln(x)} is (12e^{ln^2(x)}ln(x))/x

What is the first derivative of f(x)=6x^{ln(x)} ?

The first derivative of f(x)=6x^{ln(x)} is (12e^{ln^2(x)}ln(x))/x

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derivative of

f (x) = 6 x^{l n (x)}

\frac{12 e ^{l n^{2} (x)} ln ( x )}{x}

Solution steps

\frac{d}{d x} (6 x^{l n (x)})

Take the constant out:

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

= 6 \frac{d}{d x} (x^{l n (x)})

Apply exponent rule:

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

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

= 6 \frac{d}{d x} (e^{l n (x) l n (x)})

Apply the chain rule:

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

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

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

= 6 e^{l n (x) l n (x)} \frac{2 ln ( x )}{x}

Simplify

6 e^{l n (x) l n (x)} \frac{2 ln ( x )}{x} : \frac{12 e ^{l n^{2} (x)} ln ( x )}{x}

= \frac{12 e ^{l n^{2} (x)} ln ( x )}{x}

- \frac{5}{x ^{3}}

f (x) = 3 x + 5

\int cos^{2} (wt - k x) d x

\int \frac{1}{x ^{2} - 4} d x

x \to 0 + lim (lo g_{2} (x))

What is the derivative of f(x)=6x^{ln(x)} ?
The derivative of f(x)=6x^{ln(x)} is (12e^{ln^2(x)}ln(x))/x
What is the first derivative of f(x)=6x^{ln(x)} ?
The first derivative of f(x)=6x^{ln(x)} is (12e^{ln^2(x)}ln(x))/x