Free Math tool · Step by step

Derivative & Integral Calculator

Differentiate or integrate polynomials, powers, sin, cos, eˣ and ln x step by step — power, sum, constant and chain-rule steps shown. Free calculus helper for AP Calculus, A-level and JEE.

Try:

Derivative

ddx(3x2+2sin⁡(x)−5)=6x+2cos⁡(x)\frac{d}{dx}\left(3x^{2} + 2\sin(x) - 5\right) = 6x + 2\cos(x)
  1. 1

    Read the expression

    Interpreted as 3 terms in x.

    f(x)=3x2+2sin⁡(x)−5f(x) = 3x^{2} + 2\sin(x) - 5
  2. 2

    Sum rule

    The derivative of a sum/difference is the sum/difference of the derivatives, and constant factors stay in front.

    ddx(3x2+2sin⁡(x)−5)=ddx(3x2)+ddx(2sin⁡(x))−ddx(5)\frac{d}{dx}\left(3x^{2} + 2\sin(x) - 5\right) = \frac{d}{dx}\left(3x^{2}\right) + \frac{d}{dx}\left(2\sin(x)\right) - \frac{d}{dx}\left(5\right)
  3. 3

    Power rule on 3x^2

    Bring the exponent down and lower it by 1: d/dx(k·xⁿ) = k·n·xⁿ⁻¹.

    ddx(3x2)=3⋅2 x2−1=6x\frac{d}{dx}\left(3x^{2}\right) = 3 \cdot 2\, x^{2 - 1} = 6x
  4. 4

    Derivative of sin in 2sin(x)

    d/dx sin(u) = cos(u) (here u = x).

    ddx(2sin⁡(x))=2cos⁡(x)\frac{d}{dx}\left(2\sin(x)\right) = 2\cos(x)
  5. 5

    Constant rule on -5

    The derivative of a constant is 0.

    ddx(−5)=0\frac{d}{dx}\left(-5\right) = 0
  6. 6

    Final answer

    f′(x)=6x+2cos⁡(x)f'(x) = 6x + 2\cos(x)

AI video explanation

Want a 1-minute AI video explanation, or have a harder homework screenshot?

Doubtclip turns the question into a step-by-step whiteboard video with voice.

Click here — solve with AI

FAQ

Which functions are supported?

Sums of terms like k·xⁿ, k·sin(ax), k·cos(ax), k·e^(ax), k/x and k·ln(x). Harder expressions can be sent to the AI video solver.

Does it add the constant of integration?

Yes — every indefinite integral ends with + C.

More free tools

MathQuadratic Formula CalculatorDiscriminant, nature of roots and both roots with every step shown.MathMatrix Multiplication CalculatorInteractive grids with each row-by-column product written out.PhysicsProjectile Motion CalculatorTime of flight, max height and range from speed, angle and height.PhysicsSUVAT / Kinematics CalculatorEnter any three of s, u, v, a, t — see which equation finds the rest.