Quandaries and Queries


I am a parent trying to understand higher level of maths and would be very grateful if you could help with differentiating the following functions, identifying general rules of calculus:

a)   f(x)=e2xIn(cos(8x))

b)    f(x)=secx/SQRT(x4+1)




In the first problem you have a product of an exponential function and a log function. The power of the exponential is 2x and the derivative of 2x is 2x ln(2) so

f'(x) = d/dx[e2x] ln (cos(8x)) + e2x d/dx[In(cos(8x))]

= e2x 2x ln(2) ln (cos(8x)) + e2x [1/cos(8x)] (-sin(8x)) (8)

For the second problem I would use the quotient rule so the numerator of the derivative is

SQRT(x4+1)  d/dx[secx] - secx  d/dx[SQRT(x4+1)]

= SQRT(x4+1) secx tanx - secx (x4+1)-1/2 4x3

and the denominator is ( x4+1)



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