4.B Symbolic Differentiation
Activities
Basic Derivative Practice
Find the derivative for each of the following functions.
- \(W(r) = r^3 + 5r - 12\)
- \(f(x) = x^2 - 3\ln x\)
- \(P(t) = 4t^2 + 7\sin t\)
- \(f(x) = 1/x^2 + 5\sqrt{x} - 7\)
- \(s(x) = 2e^{x} + x^2\)
- \(h(\theta) = 1/\sqrt[3]{\theta}\)
- \(b(t) = t^2 + 5\cos t\)
More Basic Derivative Practice
Find the derivative for each of the following functions.
- \(g(x) = -\frac{1}{2}\left(x^5 +2x -9 \right)\)
- \(s(t) = 6t^{-2} + 3t^3 - 4t^{1/2}\)
- \(q(x) = 3x - 2\cdot 4^x\)
- \(y(x) = \sqrt{x}(x+1)\)
- \(P(t) = 3000(1.02)^t\)
- \(f(x) = 2^x + x^2 + 1\)
- \(d(r) = Ae^{r} - Br^2 + C\)
- \(s(t) = t^2 + 2\ln t\)
- \(g(x) = 2x - \frac{1}{\sqrt[3]{x}} + 3^x - e\)
- \(y(g) = 5\sin g - 5g + 4\)
Solutions
Basic Derivative Practice
- \(W'(r) = 3r^2 + 5\)
- \(f'(x) = 2x - 3/x\)
- \(P'(t) = 8t + 7\cos t\)
- \(f'(x) = -2x^{-3} + \frac{5}{2}x^{-1/2}\)
- \(s'(x) = 2e^{x} + 2x\)
- \(h'(\theta) = -\frac{1}{3}\theta^{-4/3}\)
- \(b'(t) = 2t - 5\sin t\)
More Basic Derivative Practice
- \(g'(x) = -\frac{1}{2}(5x^4 + 2)\)
- \(s'(t) = -12 t^{-3} + 9t^2 -2t^{-1/2}\)
- \(q'(x) = 3 - 2\cdot \ln 4 \cdot 4^x\)
- \(y'(x) = \frac{3}{2}x^{1/2} + \frac{1}{2}x^{-1/2}\)
- \(P'(t) = 3000\cdot \ln 1.02 \cdot (1.02)^t\)
- \(f'(x) = \ln 2 \cdot 2^x + 2x\)
- \(d'(r) = Ae^{r} - 2Br\)
- \(s'(t) = 2t + 2/t\)
- \(g'(x) = 2 + \frac{1}{3}x^{-4/3} + \ln 3 \cdot 3^x\)
- \(y'(g) = 5\cos g - 5\)