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dinie fofinie
Lv 5
dinie fofinie asked in Science & MathematicsMathematics · 1 decade ago

calculus 1 question:?

Find the derivative of the function.

y = 8 ^ [ cos(πx) ]

i know i need to use the chain rule but that 8 is confusing me!

thanks in advance : )

2 Answers

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  • Steiner
    Lv 7
    1 decade ago
    Favorite Answer

    If u is a differentiable function of x and f(x) = a^(u(x)), where a >0, then f'(x) = a^u ln(a) u'(x). This actually follows from the chain rule.

    Hence, y' = 8^ [ cos(πx)] ln(8) [cos(πx)]' = 8^ [ cos(πx)] ln(8) (-sin(πx) π = - ln(8) π sin(πx) 8^ [ cos(πx)]

  • John S
    Lv 5
    1 decade ago

    Convert it to the exponential function first

    y = e^(ln8 cos(pi x))

    so y' = e^(ln8 cos(pi x)) (ln8 (-sin(pi x)) (pi)

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