How do you differentiate a^x?
The quick answer is that d/dx a^x = ln(a) * a^x. But why?
Well, let's go through the steps so we can understand why the formula works.
Firstly, a^x can be written as (e^(ln(a)))^x because e^(ln(z)) = z as the natural log (ln) is the inverse of e to the power. Then we can write it as e^(x * ln a) because (a^b)^c = a^(b*c). Then differentiating e^(x * ln a) = ln(a) * a^x!
KM
Related Maths A Level answers
All answers ▸Find the first 3 terms, in ascending powers of x, of the binomial expansion of (2 – 9x)^4 giving each term in its simplest form.
Show that x^2 - 8x +17 <0 for all real values of x
If z1 = 3+2i, z2= 4-i, z3=1+i, find and simplify the following: a) z1 + z2, b) z2 x z3, c)z2* (complex conugate of z2), d) z2/z3.
∫6e^(2x+1) dx, find integral