How do you find the derivative of 9 to the 5x?

Answer 1

95x?

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

d/dx(95x)=95x*ln(9)*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(95x)=95x*ln(9)*(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(95x)=95x*ln(9)*(5*1)

d/dx(95x)=95x*ln(9)*(5)

-95x can simplify to (95)x, which equals 59049x.

-ln(9) can simplify to ln(32), so you can take out the exponent to have 2ln(3).

d/dx(95x)=59049x*2ln(3)*(5)

d/dx(95x)=10*59049x*ln(3)