Enter Function
Formulas
Basic trigonometric derivatives:
$$\frac{d}{dx}\sin(u)=\cos(u)\,u', \quad \frac{d}{dx}\cos(u)=-\sin(u)\,u', \quad \frac{d}{dx}\tan(u)=\sec^2(u)\,u'.$$
$$\frac{d}{dx}\cot(u)=-\csc^2(u)\,u', \quad \frac{d}{dx}\sec(u)=\sec(u)\tan(u)\,u', \quad \frac{d}{dx}\csc(u)=-\csc(u)\cot(u)\,u'.$$
Chain rule: $$\frac{d}{dx}f(g(x)) = f'(g(x))\cdot g'(x).$$
Product rule: $$\frac{d}{dx}[u\cdot v] = u'v + uv'.$$ Quotient rule: $$\frac{d}{dx}\left[\frac{u}{v}\right] = \frac{u'v-uv'}{v^2}.$$
General power: $$\frac{d}{dx}\big(f(x)^{g(x)}\big)=f(x)^{g(x)}\left(g'(x)\ln f(x)+g(x)\frac{f'(x)}{f(x)}\right).$$
Result
Enter a function and press Differentiate to see the first derivative.
How to write inputs
- Multiplication must be explicit: write 3*x not 3x.
- Powers: x^2, (sin(x))^2, 2^x, or general f(x)^g(x).
- Constants: pi, e. Other symbols become constants wrt the chosen variable.
- Supported functions: sin, cos, tan, cot, sec, csc, ln, log, exp, sqrt.
Frequently Asked Questions
It focuses on trigonometric forms including sin cos tan cot sec and csc along with algebraic combinations sums products quotients powers and common companions such as ln log exp and sqrt.
Yes. Change the variable field to any single identifier. Other letters become constants during differentiation.
Write sin(3*x). The chain rule is applied automatically so the derivative becomes cos(3*x)*3.
Yes. It uses the logarithmic differentiation formula f(x)^g(x) * ( g'(x) ln f(x) + g(x) f'(x)/f(x) ).
Numeric evaluation can be undefined if the point falls outside the function domain such as division by zero or logs of nonpositive numbers.
The simplifier applies arithmetic folding and basic identities like removing zeros and ones. It avoids aggressive algebra to preserve correctness.
Yes. Use pi and e. They are recognized as 3.14159... and 2.71828... respectively.
This version concentrates on correct symbolic rules and LaTeX rendering. Future enhancements may include human friendly step listings for each rule application.