4.B Symbolic Differentiation

Activities

Basic Derivative Practice

Find the derivative for each of the following functions.

  1. \(W(r) = r^3 + 5r - 12\)
  2. \(f(x) = x^2 - 3\ln x\)
  3. \(P(t) = 4t^2 + 7\sin t\)
  4. \(f(x) = 1/x^2 + 5\sqrt{x} - 7\)
  5. \(s(x) = 2e^{x} + x^2\)
  6. \(h(\theta) = 1/\sqrt[3]{\theta}\)
  7. \(b(t) = t^2 + 5\cos t\)

More Basic Derivative Practice

Find the derivative for each of the following functions.

  1. \(g(x) = -\frac{1}{2}\left(x^5 +2x -9 \right)\)
  2. \(s(t) = 6t^{-2} + 3t^3 - 4t^{1/2}\)
  3. \(q(x) = 3x - 2\cdot 4^x\)
  4. \(y(x) = \sqrt{x}(x+1)\)
  5. \(P(t) = 3000(1.02)^t\)
  6. \(f(x) = 2^x + x^2 + 1\)
  7. \(d(r) = Ae^{r} - Br^2 + C\)
  8. \(s(t) = t^2 + 2\ln t\)
  9. \(g(x) = 2x - \frac{1}{\sqrt[3]{x}} + 3^x - e\)
  10. \(y(g) = 5\sin g - 5g + 4\)

Product Rule and Quotient Rule Practice

Find the derivative for each of the following functions.

  1. \(s(t)=(t^2+4)(5t-1)\)
  2. \(y(x)=x^2\ln x\)
  3. \(g(x)= \frac{25x^2}{e^x}\)
  4. \(y(x)=x^2\cos x\)
  5. \(h(t)=\frac{t+4}{t-4}\)

Solutions

Basic Derivative Practice

  1. \(W'(r) = 3r^2 + 5\)
  2. \(f'(x) = 2x - 3/x\)
  3. \(P'(t) = 8t + 7\cos t\)
  4. \(f'(x) = -2x^{-3} + \frac{5}{2}x^{-1/2}\)
  5. \(s'(x) = 2e^{x} + 2x\)
  6. \(h'(\theta) = -\frac{1}{3}\theta^{-4/3}\)
  7. \(b'(t) = 2t - 5\sin t\)

More Basic Derivative Practice

  1. \(g'(x) = -\frac{1}{2}(5x^4 + 2)\)
  2. \(s'(t) = -12 t^{-3} + 9t^2 -2t^{-1/2}\)
  3. \(q'(x) = 3 - 2\cdot \ln 4 \cdot 4^x\)
  4. \(y'(x) = \frac{3}{2}x^{1/2} + \frac{1}{2}x^{-1/2}\)
  5. \(P'(t) = 3000\cdot \ln 1.02 \cdot (1.02)^t\)
  6. \(f'(x) = \ln 2 \cdot 2^x + 2x\)
  7. \(d'(r) = Ae^{r} - 2Br\)
  8. \(s'(t) = 2t + 2/t\)
  9. \(g'(x) = 2 + \frac{1}{3}x^{-4/3} + \ln 3 \cdot 3^x\)
  10. \(y'(g) = 5\cos g - 5\)

Product Rule and Quotient Rule Practice

  1. \(s'(t) = 2t(5t-1) + (t^2+4)5\)
  2. \(y'(x) = 2x\ln x + x^2 \cdot 1/x\)
  3. \(f'(x) = 50xe^{-x} - 25x^2e^{-x}\)
  4. \(y'(x) = 2x\cos x - x^2\sin x\)
  5. \(h'(t) = \frac{(t-4) - (t+4)}{(t-4)^2}\)