How is this page different from the derivative solver?

This page targets the process of differentiating and selecting rules. The derivative page is organized around finding and interpreting derivative results.

Can I ask for a particular differentiation rule?

Yes. Ask to use the product, quotient, chain, or another named rule and include the full expression.

Can it differentiate with respect to another variable?

Yes. Explicitly state the variable, especially when the expression contains more than one.

Purpose-built solver page

Differentiation Solver

Use this differentiation solver when the main task is how to differentiate an expression. It focuses on recognizing the structure, choosing differentiation rules, and explaining each rule application.

Type or upload a problemWorked explanationsNo sign-up required

Solve a problem now

differentiation solver

d/dx [f(x)]

Rule selection

Composite functions

Products and quotients

differentiation solver

Solve your differentiation problem

Enter your differentiation problem below. Add the variable, conditions, and method you want so the AI can return a more relevant worked response.

Text inputImage upload

Drop files to Attach, orbrowse

Step

How to use the Differentiation solver

A complete prompt usually produces a more useful explanation than an isolated expression.

1
Name the variable
d/dx
Write the expression and say which variable to differentiate with respect to.
2
Map the structure
u(g(x))
Identify sums, products, quotients, and nested functions before doing algebra.
3
Apply one rule at a time
rule₁ → rule₂
Keep intermediate derivatives visible so chain-rule factors are not lost.
4
Simplify last
f′(x)
After the derivative is established, simplify without changing its domain unexpectedly.

differentiation solver

What this Differentiation solver is designed for

The page is organized around the problem types people actually search for, while staying within the text-and-image solver's current capabilities.

(3x² − 1)⁵

u⁵

u = 3x² − 1

5u⁴ · 6x

Rule selection

d/dx [u + v]

Identify whether power, product, quotient, chain, or implicit differentiation is needed.

Composite functions

d/dx [f(g(x))]

Work from the outer function inward and keep each chain-rule factor visible.

Products and quotients

d/dx [u · v]

Differentiate the parts separately before combining them with the correct formula.

Repeated differentiation

dⁿ/dxⁿ [f(x)]

Continue from the first derivative when a second or higher derivative is requested.

Example

Differentiation problems to try

These examples reflect common search intent and can be inserted into the solver as a starting point.

Example 1

Differentiate (3x^2 - 1)^5 with respect to x

A composite function centered on the chain rule.

Example 2

Differentiate x^3 ln(x)

A product-rule problem with a logarithmic factor.

Example 3

Differentiate (x^2 + 1) / (x - 4)

A quotient-rule problem where the numerator can be simplified afterward.

Common mistakes to watch for

A worked answer is most useful when you know which details are easy to lose along the way.

Missing the inner derivative

The chain rule multiplies by the derivative of the inner function.

Misreading a product

The derivative of fg is f'g + fg', not f'g'.

Simplifying too early

Premature algebra can hide the function structure and make the right rule harder to see.