Example 29

Find the slope of a tangent line to the curve y = ( x² – 2 )⁴ at the point (1, 1). Also find its equation.

Solution : y = ( x² – 2 )⁴ ....... Given curve

Differentiating w.r.to x we get,

= 4 (x² – 2 )³

= 4 (x² – 2 )³ (2x)

= 8x (x² – 2 )3

Index

4. 1 Derivability At A Point
4. 2 Derivability In An Interval
4. 3 Derivability And Continuity Of A Function At A Point
4. 4 Some Counter Examples
4. 5 Interpretation Of Derivatives
4. 6 Theorems On Derivatives (differentiation Rules)
4. 7 Derivatives Of Standard Functions
4. 8 Derivative Of A Composite Function
4. 9 Differentiation Of Implicit Functions
4.10 Derivative Of An Inverse Function
4.11 Derivatives Of Inverse Trigonometric Functions
4.12 Derivatives Of Exponential & Logarithmic Functions
4.13 Logarithmic Differentiation
4.14 Derivatives Of Functions In Parametric Form
4.15 Higher order Derivatives

Chapter 5

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