Differentiation — Class 12 Maharashtra HSC Mathematics revision notes
A 4-page visual revision sheet for Differentiation, written for Class 12 Maharashtra HSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
What this Differentiation sheet covers
- Derivative of a Composite Function
- Standard composite derivatives
- power of a function
- sine of a function
- exponential of a function
- log of a function
- Chain rule through a square root
- Chain rule stacked two deep
- Product and quotient still apply first
- Geometrical Meaning of the Derivative
- Derivative of an Inverse Function
- if y=f(x) is differentiable with dy/dx not 0, and x=f^-1(y) exists
- Derivative of an inverse function at a point
- Derivatives of Inverse Trigonometric Functions
- y=sin^-1x, |x|<1
- y=cos^-1x, |x|<1
- y=tan^-1x, any real x
- y=cot^-1x, any real x
- y=sec^-1x, x>1
- y=cosec^-1x, x>1
- Inverse trig via a trig substitution
- Substitutions worth memorising
- Logarithmic Differentiation
- for y=[f(x)]^g(x), take log of both sides first
- then differentiate implicitly and multiply back by y
- Logarithmic differentiation with a variable exponent
- Implicit Functions
- Implicit differentiation
- Derivatives of Parametric Functions
- x=f(t), y=g(t), both differentiable in the parameter t
- Parametric differentiation
- Differentiating One Function w.r.t. Another
- Higher Order Derivatives
- Second derivative of a polynomial
- nth derivative of standard functions
- power function, m a positive integer, m>=n
- reciprocal of a linear function
- log of a linear function
- sine, phase shifted
- cosine, phase shifted
- exponential of a linear function
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Differentiation the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.