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 \[ f(y) = - 2 m^{4} y + 4 y^{3} - 3 y^{2} - 6, \]

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

  2. Compute the derivative, $\frac{df}{dx}$, of the function $f(x)$ below \[ f(x) = \ln{\left (4 x^{2} - 2 x + 1 \right )}. \]
    $f'(x) = $

  3. Compute the derivative, $\diff{ f }{ x }$, of the function \[ f(x) = \left(x^{4} + 9 x - 3\right)^{7}. \] $f'(x) = $

  4. Let $\displaystyle v(t) = \frac{3 t - 7}{2 \ln{\left (t \right )}}$. Find $\displaystyle \frac{d v}{d t}$.

    $\displaystyle \frac{d v}{d t} = $

    Need help?

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

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Math 1241, Fall 2020