The integral of a^u where u is a function of x is given as
1/ln(a) a^u + C
but if I take the derivative of that using the product rule we have C=0 because it's a constant and the derivative of 1/ln(a) = 0
so f'g=0 and for fg' we have
ua^(u-1)/ln(a) which does not look equal to a^u (but maybe it is).
I'm assuming u is a function of x but I'm setting it as u = x so that u' =1
taking the derivative of the integral should give back the original integral function correct? what am I doing wrong?
thanks!
The integral with respect to what variable? The integral of e^u with respect to u is (1/ln(a))a^u+ C:
The integral with respect to x will depend upon exactly what function of x u is.
Why use the product rule? Here 1/ln(a) is a constant and the rule (Cf(x))'= Cf'(x) is much simpler.but if I take the derivative of that using the product rule we have C=0 because it's a constant and the derivative of 1/ln(a) = 0
Wrong rule. The derivative of , with respect to u, is but that only applies when the variable is in the base and the exponent is constant. The derivative of is .so f'g=0 and for fg' we have
ua^(u-1)/ln(a) which does not look equal to a^u (but maybe it is).
I'm assuming u is a function of x but I'm setting it as u = x so that u' =1
taking the derivative of the integral should give back the original integral function correct? what am I doing wrong?
thanks!