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y=f(a^x) and f(sinx)=lnx find dy/dx
Solution) dy/dx = (a^x)(lnx)f''(a^x), .........(1)but f(sinx) = lnx implies f(x) = ln(arcsinx)hence f''(x) = (1/arcsinx) (1/ ( ( 1-x^2 ) ^ ( !/2 ) ) implies f''(a^x) = (1/arcsin(a^x)) (1/ ((1-a ^ (2x)) ^ (1/2))) ............(2)hence from ...(1) &.....(2) the solution is obtained but it should br noted that the given solution exist only when x belongs to (0,1].
Complex Numbers In the radicals section we noted that we won't get a real number out of a square root of a negative number. For example √-9 isn't a real number as there is no
Important formulas d (a b )/ dx = 0 This is a constant d ( x n ) / dx = nx n -1 Power Rule d (a x ) / dx = a x l
1/a+b+x =1/a+1/b+1/x a+b ≠ 0 Ans: 1/a+b+x =1/a+1/b+1/x => 1/a+b+x -1/x = +1/a +1/b ⇒ x - ( a + b + x )/ x ( a + b + x ) = + a + b/ ab ⇒
Is it possible to add two vectors of unequal magnitude and get a resultant of zero?Please explain also. Ans) no it is not possible as .. if the magnitude is diffrent then they c
Find out the number of ways in which 5 prizes can be distributed among 5 students such that (a) Each student may get a prize. (b) There is no restriction to the number o
compare: 643,251: 633,512: 633,893. The answer is 633,512.
When there are 4 dots how many chords are they
100+5000
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Negative Skewness It is an asymmetrical curve whether the long tail extends to the left NB: In developed countries this frequency curve for the age distribution is charact
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