What is the derivative of x^27^x ?

The derivative of x^27^x is 2x*7^x+7^xln(7)x^2

What is the first derivative of x^27^x ?

The first derivative of x^27^x is 2x*7^x+7^xln(7)x^2

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

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

Solution steps

\frac{d}{d x} (x^{2} \cdot 7^{x})

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (7^{x}) = 7^{x} ln (7)

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

\int \frac{5 x}{( x ^{2} + 2 ) ^{2}} d x

\int_{- 1}^{1} (2 1 - x^{2})^{2} d x

3 sec (3 x)

What is the derivative of x^27^x ?
The derivative of x^27^x is 2x*7^x+7^xln(7)x^2
What is the first derivative of x^27^x ?
The first derivative of x^27^x is 2x*7^x+7^xln(7)x^2