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=(cos.x)sin x +sin x(cos.x), , =2sin xcosx=sin2x , Find the derivative of x* — 2 at x = 10., , Find the derivative of x at x= 1., , Find the derivative of 99x at x = 100., , Find the derivative of the following functions from first principle., , @ 8-27 (ii), (x-1)(x-2), , Pers, , wy © ayy) 2th, a) = i, , 5. For the function, , f(x), , 100 2, , x” x, —+...4 4x41., , =—~+, 100 99, , 2020-21, , LIMITS AND DERIVATIVES, 313, , Prove that f’(1)=100f’(0)., , 6. Find the derivative of x" +ax"!+a?x"*+...+a"'x+a" for some fixed real, , number a., 7. For some constants a and b, find the derivative of, , , , , , 5 2 wa. X74, (i) (x-a) (x-b) (ii) (ax? +b) (iii) xb., x"-a", 8. Find the derivative of for some constant a., 9. Find the derivative of, . 3 - 3, (i) iy (ii) (5x +3x-1) (x-1), (ii) x9 (5+3x) (iv) x*(3=6x°), -4 “6 . 2 x, 3-4. ———, Wie ( es ) wy} x+1l 3x-1, 10. Find the derivative of cos x from first principle., 11. Find the derivative of the following functions:, (i) sinxcos x (ii) secx (iii) Ssecx+4cos x, (iv) cosec x (v) 3cotx+Scosecx, (vi) Ssinx-6cosx+7 (vii) 2tanx—7secx, Miscellaneous Examples, , Example 19 Find the derivative of f from the first principle, where f is given by, 2x+3 - id