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

##### 1 Answer

May 6, 2017

# 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 ) #