Math Insight

Basic derivative practice

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  1. Let $\displaystyle r(y) = \frac{5 y - 9}{2 \ln{\left (y \right )}}$. Find $\displaystyle r'(y)$.

    $\displaystyle r'(y) = $

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  2. Compute the derivative, $\diff{f}{x}$, of the function $f(x)$ below \[ f(x) = \left(x^{2} - 4 x + 4\right) e^{x}. \] $f'(x) = $

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

  4. Given that $n$ is a constant parameter, compute the derivative, $g'(x)$, of \[ g(x) = 4 n^{5} x + 4 x^{3} - 3 x^{2} - 5, \]

    $\displaystyle g'(x) = $

  5. Compute the derivative, $\diff{ f }{ x }$, of the function \[ f(x) = \left(x^{3} - 3 x + 4\right)^{6}. \] $f'(x) = $

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Math 201, Spring 22