# Questions with detailed step by step solutions from Differential Calculus

##### Topics covered under Differential Calculus

Real - valued functions, algebra of functions, polynomials, rational, trigonometric, logarithmic and exponential functions, inverse functions. Graphs of simple functions. Limits, continuity and differentiability. Differentiation of the sum, difference, product and quotient of two functions. Differentiation of trigonometric, inverse trigonometric, logarithmic, exponential, composite and implicit functions; derivatives of order upto two. Rolle’s and Lagrange’s Mean Value Theorems. Applications of derivatives: Rate of change of quantities, monotonic - increasing and decreasing functions, Maxima and minima of functions of one variable, tangents and normals.

Direct Method
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Standard Simplifications
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Sandwich Theorem and Trigonometric Functions
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L'Hospital's Rule
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Limit of Exponential and Logarithmic Function
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Limits of Special Functions
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Discontinuity of a Function
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Algebra of Continuous Functions
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Derivatives
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First Principle of Differentiation
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Logarithmic Differentiation
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Differentiation of Implicit Functions
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Differentiation by Substitution
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Differentiation of an Infinite Expression
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Higher Order Derivatives
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Differentiation of Determinants
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Rolle's Theorem and Intermediate Value Theorem
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Lagrange's Mean Value Theorem
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Taylor's and Maclaurin's Series
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Rate Measurement
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Approximations and Differentials
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Nature of the Function
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Maxima and Minima
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Applications on Geometrical Figures
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Continuity of a Function
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Continuity and Differentiability
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Algebra of Derivative of Functions
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Chain and Reciprocal Rule
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Differentiation of Functions in Parametric Form
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Nature of Roots of Polynomial Function
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