# APPLICATIONS OF DERIVATIVES

**Syllabus**

**6.1 Derivatives**: derivative of inverse trigonometric, exponential and logarithmic function by definition, relationship between continuity and differentiability, rules for differentiating hyperbolic function and inverse hyperbolic function, L’Hospital's rule (0/0, ∞/∞), differentials, tangent and normal, geometrical interpretation and application of Rolle’s theorem and mean value theorem.

**Learning Outcomes**

**6. Calculus:**

6.1 find the derivatives of inverse trigonometric, exponential and logarithmic functions by definition.

6.2 establish the relationship between continuity and differentiability.

6.3 differentiate the hyperbolic function and inverse hyperbolic function

6.4 evaluate the limits by L'hospital's rule (for 0/0, ∞/∞).

6.5 find the tangent and normal by using derivatives.

6.6 interpret geometrically and verify Rolle's theorem and Mean Value theorem.

6.7 find the anti-derivatives of standard integrals, integrals reducible to standard forms and rational function (using partial fractions also).

6.8 solve the differential equation of first order and first degree by separable variables, homogenous, linear and exact differential equations

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** EXERCISE **

## DIFFERENTIALS

## TANGENTS AND NORMALS

## L HOSPITAL'S RULE