📐 Derivatives & Tangent Lines Visualizer
CalculusWhat's happening? The tangent line's slope at any point = f'(x). For f(x) = x², the derivative is 2x. Move the point and watch the tangent rotate.
Calculus: 12-15 questions every year. Highest weightage.
JEE tests derivative definition, chain rule, tangent/normal equations.
Key formulas
Derivatives & Tangent Lines Formulas
Definition
f'(x) = lim[f(x+h)-f(x)]/h
Slope of tangent
Chain rule
dy/dx = dy/du x du/dx
Composite functions
Tangent
y - y1 = f'(x1)(x - x1)
At point (x1,y1)
Product rule
(uv)' = u'v + uv'
Product of functions
Step-by-step problem solving
How to solve maths problems in JEE
- Identify function type
- Apply differentiation rule
- Evaluate f'(a) for slope
- Tangent: y-y1 = m(x-x1), Normal: y-y1 = -1/m(x-x1)
Common JEE mistakes
What students get wrong
Missing chain rule
sin(x^2) = cos(x^2)*2x, not just cos(x^2)
Normal slope sign
m_normal = -1/m_tangent
dy/dx vs dx/dy
dy/dx = 1/(dx/dy)
Implicit diff
y^2 derivative = 2y*dy/dx
FAQs
Derivatives & Tangent Lines Questions
Equation of tangent?
f'(x), slope at a, point (a,f(a)), y-f(a) = f'(a)(x-a)
Derivative geometrically?
Slope of tangent, rate of change
Normal parallel to x-axis?
When tangent vertical, f'(a) undefined
Increasing function?
f'(x) > 0 in that interval