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Derivative of:
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Derivative of x^sin(x)
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Derivative of 4/x^2
Identical expressions
y=(x^ two)(a^x)
y equally (x squared )(a to the power of x)
y equally (x to the power of two)(a to the power of x)
y=(x2)(ax)
y=x2ax
y=(x²)(a^x)
y=(x to the power of 2)(a to the power of x)
y=x^2a^x

The derivative of the function/ y=(x^2)(a^x)

Derivative of y=(x^2)(a^x)

The solution

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 2  x
x *a

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

x^2*a^x

Detail solution

Apply the product rule:

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

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

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

The answer is:

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

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify