What is the derivative of 2 to the power of 5x?

Answer 1

25x?

d/dx(au)=au*ln(a)*d/dx(u)

d/dx(25x)=25x*ln(2)*d/dx(5x)

-The derivative of 5x is:

d/dx(cu)=c*du/dx where c is a constant

d/dx(5x)=5*d/dx(x)

d/dx(25x)=95x*ln(2)*(5*d/dx(x))

-The derivative of x is:

d/dx(x)=1x1-1

d/dx(x)=1*x0

d/dx(x)=1*(1)

d/dx(x)=1

d/dx(25x)=25x*ln(2)*(5*1)

d/dx(25x)=25x*ln(2)*(5)

-25x can simplify to (25)x, which equals 32x.

d/dx(95x)=32x*ln(2)*(5)