What is the derivative of 3x^{ln(x}) ?

The derivative of 3x^{ln(x}) is (6e^{ln^2(x)}ln(x))/x

What is the first derivative of 3x^{ln(x}) ?

The first derivative of 3x^{ln(x}) is (6e^{ln^2(x)}ln(x))/x

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\frac{d}{d x} (3 x^{l n (x)})

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

Solution steps

\frac{d}{d x} (3 x^{l n (x)})

Take the constant out:

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

= 3 \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)}

= 3 \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}

= 3 e^{l n (x) l n (x)} \frac{2 ln ( x )}{x}

Simplify

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

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

(x, y) \to (- 1, 1) lim (x + y)

\int_{0}^{1} \frac{x ^{3}}{1 + x ^{3}} d x

\frac{d}{d t} (- 2 cos (t))

y^{^{''}} = - a y

\frac{d}{d x} (- 2 cos (- 3 x + 7))

What is the derivative of 3x^{ln(x}) ?
The derivative of 3x^{ln(x}) is (6e^{ln^2(x)}ln(x))/x
What is the first derivative of 3x^{ln(x}) ?
The first derivative of 3x^{ln(x}) is (6e^{ln^2(x)}ln(x))/x