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If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 3.1 : The Definition of the Derivative
Use the definition of the derivative to find the derivative of the following functions.
- \(g\left( x \right) = 10\)
- \(T\left( y \right) = - 8\)
- \(f\left( x \right) = 5x + 7\)
- \(Q\left( t \right) = 1 - 12t\)
- \(f\left( z \right) = {z^2} + 3\)
- \(R\left( w \right) = {w^2} - 8w + 20\)
- \(V\left( t \right) = 6t - {t^2}\)
- \(Q\left( t \right) = 2{t^2} - 8t + 10\)
- \(g\left( z \right) = 1 + 10z - 7{z^2}\)
- \(f\left( x \right) = 5x - {x^3}\)
- \(Y\left( t \right) = 2{t^3} + 9t + 5\)
- \(Z\left( x \right) = 2{x^3} - {x^2} - x\)
- \(\displaystyle f\left( t \right) = \frac{2}{{t - 3}}\)
- \(\displaystyle g\left( x \right) = \frac{{x + 2}}{{1 - x}}\)
- \(\displaystyle Q\left( t \right) = \frac{{{t^2}}}{{t + 2}}\)
- \(f\left( w \right) = \sqrt {w + 8} \)
- \(V\left( t \right) = \sqrt {14 + 3t} \)
- \(G\left( x \right) = \sqrt {2 - 5x} \)
- \(Q\left( t \right) = \sqrt {1 + 4t} \)
- \(f\left( x \right) = \sqrt {{x^2} + 1} \)
- \(\displaystyle W\left( t \right) = \frac{1}{{\sqrt t }}\)
- \(\displaystyle g\left( x \right) = \frac{4}{{\sqrt {1 - x} }}\)
- \(f\left( x \right) = x + \sqrt x \)
- \(\displaystyle f\left( x \right) = x + \frac{1}{x}\)