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Trig Derivative Calculator

Differentiate A f(kx + b) for common trigonometric functions

Trig Derivative Formulas

d/dx sin u = cos u · u', d/dx cos u = -sin u · u', d/dx tan u = sec^2 u · u'

For A f(kx+b), the derivative is A times the derivative of f(u), multiplied by u' = k.

This tool handles basic trig functions with a linear inner angle. More complex products or powers need product, quotient, or chain rules.

How Trig Differentiation Works

Trig derivatives combine memorized derivative formulas with the chain rule for inner angles.

Outer Function

Choose the derivative rule for sin, cos, tan, sec, csc, or cot.

Inner Angle

Let u = kx + b and compute u' = k.

Coefficient

The outside coefficient A multiplies the final derivative.

Final Form

Keep the same inner expression inside the resulting trig function.

Example: d/dx [2 sin(3x)] = 2 · cos(3x) · 3 = 6 cos(3x).

Applications

CalculusMotionWave ModelsOptimization

Frequently Asked Questions

What are the basic trig derivatives?
d/dx sin x = cos x, d/dx cos x = -sin x, d/dx tan x = sec^2 x, d/dx sec x = sec x tan x, d/dx csc x = -csc x cot x, and d/dx cot x = -csc^2 x.
When is the chain rule needed?
Use the chain rule when the angle is not simply x, such as sin(3x+2). Multiply the derivative of the outside function by the derivative of the inner expression.
Can this calculator handle a linear angle?
Yes. It supports forms like A sin(kx+b), A cos(kx+b), and similar basic trigonometric functions.

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