Math Insight

Basic derivative practice

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  1. Given that $m$ is a constant parameter, compute the derivative, $\frac{d f}{d y}$, of \[ f(y) = - 4 m^{3} y + 7 y^{3} - 3 y^{2} - 2, \]

    $\displaystyle \frac{d f}{d y} = $

  2. Calculate $\displaystyle r'(t)$, where $\displaystyle r(t) = \frac{4 t - 8}{t + 2}$.

    $\displaystyle r'(t) = $

    Need help?

  3. Compute the derivative, $\frac{df}{dx}$, of the function $f(x)$ below \[ f(x) = \left(6 x^{2} + 3 x\right) \ln{\left (x \right )}. \] $f'(x) = $

  4. Compute the derivative, $\diff{ f }{ x }$, of the function \[ f(x) = \left(x^{4} + x + 10\right)^{8}. \] $f'(x) = $

  5. Compute the derivative, $\frac{df}{dx}$, of the function $f(x)$ below \[ f(x) = e^{x^{2} - 2 x}. \] $f'(x) = $

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Math 201, Spring 2017