I have done this problem over and over again and have about four different answers. Could someone help me out and tell me what they get? I get so far and then my work changes and I don't know which way is right!! Thanks so much.
[Calc 2 is the worst!]
2007-02-02 02:40:35 · 3 answers · asked by Sarah 4 in Science & Mathematics ➔ Mathematics
Take ln when you have a variable as an exponent
ln y = 5x ln(sin(7x))
The derivative of ln y = y' / y by implicit differentiation.
Use the product rule to derivate the right side:
y' / y = 5x (7cos(7x)) / (sin(7x)) + ln(sin(7x)) * 5
y' / y = 35 x cot(7x) + 5 ln(sin(7x))
Multiply both sides by y:
y'=y * (35 x cot(7x) + 5 ln(sin(7x)) )
y'=(sin(7x))^(5x) * (35 x cot(7x) + 5 ln(sin(7x)) )
2007-02-02 03:42:02 · answer #1 · answered by Professor Maddie 4 · 1⤊ 0⤋
Write it as y= e^(5x*Ln(sin(7x))and use chain rule
y´= (sin(7x))^(5x) *[ 5Ln((sin(7x))+5x* 1/sin(7x) *7cos(7x) ]
2007-02-02 18:05:38 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋
it is easier than u thought. marilyn vos wouldn't blink
2007-02-02 10:44:30 · answer #3 · answered by alexis christian 2 · 0⤊ 1⤋