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Example 29
Find the slope of a tangent line to the curve y = ( x^{2 }– 2 )^{4} at the point (1, 1). Also find its equation.
Solution : y = ( x^{2 }– 2 )^{4} ....... Given curve
Differentiating w.r.to x we get,
= 4 (x^{2} – 2 )^{3}
= 4 (x^{2} – 2 )^{3 }(2x)
= 8x (x^{2} – 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