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

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

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

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

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

9 x^{3 x} (ln (x) + 1)

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

x^{3 x} = e^{3 x l n (x)}

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x ln (x)) = 3 (ln (x) + 1)

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

Simplify

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

= 9 x^{3 x} (ln (x) + 1)

\frac{d}{d x} (5 - 2 sin (x) - e^{x})

\int \frac{t}{( 3 t ^{2} + 1 ) ^{4}} d t

y^{^{'}} + y = cos (t), y (0) = 1

y = lo g_{e} (lo g_{e} (x))

h \to 0 lim (\frac{( h + 2 ) ^{3} - 8}{h})

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