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Derivative of:
Derivative of x^-(4/5)
Derivative of ln(x^2-2x)
Derivative of 2*x-x^2
Derivative of 2^x*x^2
Identical expressions
two ^x*x^ two
2 to the power of x multiply by x squared
two to the power of x multiply by x to the power of two
2x*x2
2^x*x²
2 to the power of x*x to the power of 2
2^xx^2
2xx2

The derivative of the function/ 2^x*x^2

Derivative of 2^x*x^2

The solution

You have entered [src]

 x  2
2 *x

$$2^{x} x^{2}$$

2^x*x^2

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = 2^{x}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. $\frac{d}{d x} 2^{x} = 2^{x} \log{\left(2 \right)}$
$g{\left(x \right)} = x^{2}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
The result is: $2^{x} x^{2} \log{\left(2 \right)} + 2 \cdot 2^{x} x$
Now simplify:

$2^{x} x \left(x \log{\left(2 \right)} + 2\right)$

The answer is:

$2^{x} x \left(x \log{\left(2 \right)} + 2\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     x    x  2       
2*x*2  + 2 *x *log(2)

$$2^{x} x^{2} \log{\left(2 \right)} + 2 \cdot 2^{x} x$$

Simplify

The second derivative [src]

 x /     2    2                \
2 *\2 + x *log (2) + 4*x*log(2)/

$$2^{x} \left(x^{2} \log{\left(2 \right)}^{2} + 4 x \log{\left(2 \right)} + 2\right)$$

Simplify

The third derivative [src]

 x /     2    2                \       
2 *\6 + x *log (2) + 6*x*log(2)/*log(2)

$$2^{x} \left(x^{2} \log{\left(2 \right)}^{2} + 6 x \log{\left(2 \right)} + 6\right) \log{\left(2 \right)}$$

Simplify

The graph

Derivative of 2^x*x^2