Derek K.
asked • 06/04/21Find the derivative !!WITHOUT USING FRACTIONS AND NEGATIVE EXPONENTS!!
f(x)= 6√x - 10/x^7
USE sqrt(x) for √x
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2 Answers By Expert Tutors
Shane L. answered • 06/04/21
Tutor
5.0
(340)
Experienced Mathematics/Physics/Mechanical Engineering Tutor B.S. M.S.
f'(x) = 6*(1/2)x^(-1/2) - 10(-7)x^(-8)
f'(x) = 3/sqrt(x) +70/x^8
Paul D. answered • 06/05/21
Tutor
5
(174)
PhD in Mathematics - Specializing in AP Calculus
Here could be an alternative way (using the multiplication rule only):
Let y = f(x) = 6sqrt(x) - 10/x^7
x^7y = 6x^(15/2) - 10 (Multiply both sides by x^7)
7x^7y + x^7y' = 45x^(13/2) (Differentiate both sides w.r.t. x)
x^7y' = 45x^(13/2) - 7x^7(6sqrt(x) - 10/x^7) (Substitute 6sqrt(x) - 10/x^7 for y)
y' = f'(x) = 3/sqrt(x) +70/x^8
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Mark M.
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