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

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

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

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

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

ln (3) \cdot 3^{3 x + 1} x^{3 x} + 3^{1 + 3 x} x^{3 x} (ln (x) + 1)

Solution steps

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

Simplify

(3 x)^{3 x} : 2 7^{x} x^{3 x}

= \frac{d}{d x} (2 7^{x} x^{3 x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 2 7^{x}, g = x^{3 x}

= \frac{d}{d x} (2 7^{x}) x^{3 x} + \frac{d}{d x} (x^{3 x}) 2 7^{x}

\frac{d}{d x} (2 7^{x}) = ln (3) \cdot 3^{3 x + 1}

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

= ln (3) \cdot 3^{3 x + 1} x^{3 x} + 3 x^{3 x} (ln (x) + 1) \cdot 2 7^{x}

3 x^{3 x} (ln (x) + 1) \cdot 2 7^{x} = 3^{1 + 3 x} x^{3 x} (ln (x) + 1)

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

\int \frac{1}{a + b x} d x

\frac{d}{d x} (- 4 cot (2 x) csc (2 x))

y^{^{''}} + 2 y^{^{'}} + 5 y = 4 sin (2 t)

\frac{d}{d x} (\frac{1}{3} cos (\frac{6 π x - 1}{2}))

\int x^{7} sin (x^{8}) d x

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