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

The derivative of (3x^2^{2x}) is 2ln(3)*9^xx^{4x}+2*9^xx^{4x}(2ln(x)+2)

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

The first derivative of (3x^2^{2x}) is 2ln(3)*9^xx^{4x}+2*9^xx^{4x}(2ln(x)+2)

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

2 ln (3) \cdot 9^{x} x^{4 x} + 2 \cdot 9^{x} x^{4 x} (2 ln (x) + 2)

Solution steps

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

Simplify

(3 x^{2})^{2 x} : 9^{x} (x^{2})^{2 x}

= \frac{d}{d x} (9^{x} (x^{2})^{2 x})

Apply the Product Rule:

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

f = 9^{x}, g = (x^{2})^{2 x}

= \frac{d}{d x} (9^{x}) (x^{2})^{2 x} + \frac{d}{d x} ((x^{2})^{2 x}) 9^{x}

\frac{d}{d x} (9^{x}) = 2 ln (3) \cdot 9^{x}

\frac{d}{d x} ((x^{2})^{2 x}) = 2 x^{4 x} (2 ln (x) + 2)

= 2 ln (3) \cdot 9^{x} (x^{2})^{2 x} + 2 x^{4 x} (2 ln (x) + 2) \cdot 9^{x}

(x^{2})^{2 x} = x^{4 x}

= 2 ln (3) \cdot 9^{x} x^{4 x} + 2 \cdot 9^{x} x^{4 x} (2 ln (x) + 2)

\int \frac{5 x - 4}{8 x - 5 x ^{2} + 9} d x

\int_{\frac{1}{3}}^{5} 8 x ln (3 x) d x

\frac{d}{d x} (ln (sin (x^{2})))

\frac{d}{d x} (\frac{1}{f ( x ) ^{2} ( x )})

- 10 x^{3} + 6 x^{40} y + y^{4} = 3

What is the derivative of (3x^2^{2x}) ?
The derivative of (3x^2^{2x}) is 2ln(3)*9^xx^{4x}+2*9^xx^{4x}(2ln(x)+2)
What is the first derivative of (3x^2^{2x}) ?
The first derivative of (3x^2^{2x}) is 2ln(3)*9^xx^{4x}+2*9^xx^{4x}(2ln(x)+2)