Math Insight

Basic derivative practice

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

  2. 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) = $

  3. Given that $c$ is a constant parameter, compute the derivative, $\diff{ h }{ y } $, of \[ h(y) = 2 c y + 6 y^{3} - y^{2} - 10, \]

    $\displaystyle \diff{ h }{ y } = $

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