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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].
y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3y = 0 , y (4) = 1/8 , and y'(4) = -3/64 Solution : As we noticed in previous illustration the function is a solution an
explain the basics of permutation
Connecticut state sales tax is 6%. Lucy purchases a picture frame in which costs $10.50 What is the Connecticut sales tax on this item? Find out 6% of $10.50 by multiplying $10
As we saw in the previous section computing Laplace transforms directly can be quite complex. Generally we just utilize a table of transforms when actually calculating Laplace tran
Company A and Company B have spent a lot of money on research to develop a cure for the common cold. Winter is approaching and there is certainly going to be a lot of demand for th
INTEGRAL OF X5^X
27-125 a power -135a +225a power2
Let E; F be 2 points in the plane, EF has length 1, and let N be a continuous curve from E to F. A chord of N is a straight line joining 2 points on N. Prove if 0 and N has no cho
Evaluate following. (a) 625 3/4 Solution (a) 625 3/4 Again, let's employ both forms to calculate this one. 625 3/4 =( 625 1/4 ) 3 =(5) 3 = 12
what is integration and how is it important
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