Question

How do you find the derivative of `y= x^3*2^x`?

Answer 1

`dy/dx = x^2 2^x(3+xln2 )`

Explanation:

We have;

`y = x^3 2^x`

We have a variable exponent so we must use the known result for exponents:

`d/dx e^(x) = e^x => d/dx a^x = ln * a^x`

So we can apply the product rule to get:

`dy/dx = (x^3)(d/dx 2^x) + (d/dx x^3)( 2^x)`
`" " = (x^3)(ln2 * 2^x) + (3x^2)( 2^x)`
`" " = ln2 * x^3 * 2^x + 3x^2 * 2^x`
`" " = x^2 2^x(3+xln2 )`