Partial Derivative Calculator
Calculus, Multivariable
Intro: Finds partial derivatives of multivariable functions with respect to a chosen variable, treating others as constants.
Worked example
- Find $∂f/∂x$ for $f(x, y) = x^2 y + 3x y^2 − sin(x)$.
- We have $f(x,y)=x^2y+3xy^2-\sin x$ and want the partial derivative with respect to x.
- Treat y as a constant throughout differentiation with respect to x.
- Differentiate the first term: $\dfrac{\partial}{\partial x}(x^2y) = 2xy$ because derivative of $x^2$ is $2x$ and y is constant.
- Differentiate the second term: $\dfrac{\partial}{\partial x}(3xy^2) = 3y^2$ because derivative of x is 1, and $3y^2$ is a constant factor.
- Differentiate the third term: $\dfrac{\partial}{\partial x}(-\sin x) = -\cos x$.
- Combine the results: $\dfrac{\partial f}{\partial x} = 2xy + 3y^2 - \cos x$.
- Answer: $\boxed{\dfrac{\partial f}{\partial x} = 2xy + 3y^2 - \cos x.}$
FAQs
Can it handle more than two variables?
Yes, the function can involve x, y, z, etc. You choose which variable to differentiate with respect to.
Why choose MathGPT?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
How this calculator works
- Type or paste your function (LaTeX like
\sin,\lnworks too). - Press Generate a practice question button to generate the derivative and the full reasoning.
- Review each step to understand which rule was applied and why.
- Practice with similar problems to lock in the method.