What is the derivative of 3x^{2x} ?

The derivative of 3x^{2x} is 6x^{2x}(ln(x)+1)

What is the first derivative of 3x^{2x} ?

The first derivative of 3x^{2x} is 6x^{2x}(ln(x)+1)

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derivative of

3 x^{2 x}

6 x^{2 x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (3 x^{2 x})

Take the constant out:

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

= 3 \frac{d}{d x} (x^{2 x})

Apply exponent rule:

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

x^{2 x} = e^{2 x l n (x)}

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x ln (x)) = 2 (ln (x) + 1)

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

Simplify

3 e^{2 x l n (x)} \cdot 2 (ln (x) + 1) : 6 x^{2 x} (ln (x) + 1)

= 6 x^{2 x} (ln (x) + 1)

x \to \infty lim (\frac{5 x}{x})

t^{5}

f (x) = a^{6} + cos^{6} (x)

\int \frac{x ^{3} + 1}{x ^{2} + 1} d x

y = \frac{x}{x + 1}

What is the derivative of 3x^{2x} ?
The derivative of 3x^{2x} is 6x^{2x}(ln(x)+1)
What is the first derivative of 3x^{2x} ?
The first derivative of 3x^{2x} is 6x^{2x}(ln(x)+1)