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Thank you for answering my question. I could use some help with the power rule to solve this question, very tricky:

Assume u and v are functions of x that are differentiable at x=0 and that u(0)=2, u'(0)=10, v(0)=-4 and v'(0)=-5

If f(x)=u*v, find f'(0)

To find the derivative of f(x) = u(x)･v(x), you need to use the "product rule", which is written as

f'(x) = u'(x)･v(x) + u(x)･v'(x).

Plugging in the values of u(0), v(0), u'(0), v'(0) given in your question gives

f'(0) = (10)(-4) + (2)(-5) = -40 - 10 = -50

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college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related **Publications**

J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane**Education/Credentials**

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