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Equation of a Tangent Line (Derivative)

See how to find the equation of a tangent line
by using the derivative of a function.
2 examples and their solutions.

Equation of a Tangent Line (Derivative)

Formula


y = f'(a)(x - a) + f(a)
Slope of the tangent line at x = a: f'(a)
Derivative Rules

Tangent line passes through (a, f(a)).

→ y - f(a) = f'(a)(x - a)
Linear Equation (Two Variables)

→ y = f'(a)(x - a) + f(a)

Example

f(x) = x3 - 4x2 + 7

Tangent line at x = 1?
Solution

Example

f(x) = ex

Tangent line at x = 0?
Solution