Variable powers exercises answers 2

  1. y = f(x) = 4x

    f dash of x equals (the natural logarithm of 4 )times 4 to the power of x

  2. y = f(x) = 7x − 3

    f dash of x equals (the natural logarithm of 7 )times 7 to the power of (x minus 3)

  3. y = f(x) = (x2 − 1)x + 1

    f dash of x equals (x squared minus 1) to the power of (x plus 1) times (the natural logarithm of (x squared minus 1) plus the reciprocal of (x minus 1))

  4. y = f(x) = (10 − 2x)x

    f dash of x equals x times ((10 minus 2x) to the power of (x minus 1)) plus the natural logarithm of (10 minus 2x) times ((10 minus 2x) to the power of x)

  5. y = f(x) = 10x(5x2)

    f dash of x equals (10 to the power of x) times 5 times (x squared) times the natural logarithm of 10 plus x times (10 to the power of (x plus 1))


    Alternatively this problem could be solved by using the product rule first.
    The derivative of 10x is 10x ln 10 by a similar calculation to problem 6.
    f(x) = 10x(5x2)
    f'(x) = (10x ln 10)(5x2) + (10x)(10x) = 5x210xln 10 + x10x + 1
    as before.

Close