Question

Find the derivative of the following functions from first principle. 

(i) x² 

(ii) e^-x 

(iii) log(x + 1)

Answer 1

(i) Let f(x) = x² then f(x + h) = (x + h)² 

Now \(\frac{d}{dx}\)f(x)

Thus \(\frac{d}{dx}\)(x²) = 2x

(ii) Let f(x) = e^-x then f(x + h) = e^{-(x + h)}

Now \(\frac{d}{dx}\)f(x) 

(iii) Let f(x) = log(x + 1) 

Then f(x + h) = log(x + h + 1) = log((x + 1) + h) 

Now \(\frac{d}{dx}\)f(x)