Find dydx if y=3x⋅5x .

Answer 1

To find dy/dx, we will need to use the product rule and differentiate each term separately.

Using the product rule, we know that (uv)' = u'v + uv'. Applying this to our equation:

Let u = 3x and v = 5x

Then, u' = 3 and v' = 5

Now, we can find dy/dx:

dy/dx = u'v + uv'

Taking the derivative of each term:

u'v = (3)(5x) = 15x

uv' = (3x)(5) = 15x

dy/dx = 15x + 15x

Combining like terms, we get:

dy/dx = 30x