Question

find dy/dx for y=6^x-1

Answer 1

Is it \(\Large y=6^{x-1}\)

Answer 2

y = x^-6 is also equal to y = 1 / x^6

So now we apply the quotient law of derivation: Which states if we have a function
y(x) = f(x) / g(x) then the derivative
of y(x) = y '(x) =[ f '(x)*g(x) - f(x)*g '(x) ] / ( g(x) )^2

So y '(x) = Dx[ 1 ]* x^6 - 1 * Dx[x^6] / ( x^6 )^2
= 0 * x^6 - 1*6x^5 / x^12
= 0 - 6x^5 / x^12
= -6x^5 / x^12
= -6 / x^7

Hence: y '(x) = -6 / x^7