Description
Calculate the derivative of a function with respect to a variable instantly. Derivatives are essential in calculus, physics, and engineering to determine rates of change. Simply input your function, and this calculator provides accurate results, supporting tasks in advanced mathematics, economics, and science.
Derivative Examples
1. \( f(x) = x^2 \)
Solution: \( f'(x) = 2x \)
2. \( f(x) = e^x \)
Solution: \( f'(x) = e^x \)
3. \( f(x) = \sin(x) \)
Solution: \( f'(x) = \cos(x) \)
4. \( f(x) = \cos(x) \)
Solution: \( f'(x) = -\sin(x) \)
5. \( f(x) = \ln(x) \)
Solution: \( f'(x) = \frac{1}{x} \)
6. \( f(x) = x^3 \)
Solution: \( f'(x) = 3x^2 \)
7. \( f(x) = \tan(x) \)
Solution: \( f'(x) = \sec^2(x) \)
8. \( f(x) = \sqrt{x} \)
Solution: \( f'(x) = \frac{1}{2\sqrt{x}} \)
9. \( f(x) = \frac{1}{x} \)
Solution: \( f'(x) = -\frac{1}{x^2} \)
10. \( f(x) = \ln(\sin(x)) \)
Solution: \( f'(x) = \cot(x) \)