Section 3.1 : The Definition of the Derivative
Use the definition of the derivative to find the derivative of the following functions.
- \(g\left( x \right) = 10\)
- \(T\left( y \right) = - 8\)
- \(f\left( x \right) = 5x + 7\)
- \(Q\left( t \right) = 1 - 12t\)
- \(f\left( z \right) = {z^2} + 3\)
- \(R\left( w \right) = {w^2} - 8w + 20\)
- \(V\left( t \right) = 6t - {t^2}\)
- \(Q\left( t \right) = 2{t^2} - 8t + 10\)
- \(g\left( z \right) = 1 + 10z - 7{z^2}\)
- \(f\left( x \right) = 5x - {x^3}\)
- \(Y\left( t \right) = 2{t^3} + 9t + 5\)
- \(Z\left( x \right) = 2{x^3} - {x^2} - x\)
- \(\displaystyle f\left( t \right) = \frac{2}{{t - 3}}\)
- \(\displaystyle g\left( x \right) = \frac{{x + 2}}{{1 - x}}\)
- \(\displaystyle Q\left( t \right) = \frac{{{t^2}}}{{t + 2}}\)
- \(f\left( w \right) = \sqrt {w + 8} \)
- \(V\left( t \right) = \sqrt {14 + 3t} \)
- \(G\left( x \right) = \sqrt {2 - 5x} \)
- \(Q\left( t \right) = \sqrt {1 + 4t} \)
- \(f\left( x \right) = \sqrt {{x^2} + 1} \)
- \(\displaystyle W\left( t \right) = \frac{1}{{\sqrt t }}\)
- \(\displaystyle g\left( x \right) = \frac{4}{{\sqrt {1 - x} }}\)
- \(f\left( x \right) = x + \sqrt x \)
- \(\displaystyle f\left( x \right) = x + \frac{1}{x}\)