DLS
siny=xsin(a+y)
dy/dx=?
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DLS
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I have a small doubt here..
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is xsin(a+y) to be solved with product rule?
lgbasallote
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dy/dx means you take the derivative of x... since sin(a+y) does not include any x in it... no, you don't use product rule. you treat sin(a+y) as a constant coefficient
DLS
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:o?
hartnn
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ummm.... u need to use product rule...
DLS
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I did..
hartnn
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because y is the function of x
DLS
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What I want to ask is..if I had ysin(a+y) then I wuldve used chain rule?
lgbasallote
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you only use product rule when two facots include x
for example
xsin x <-- x and sinx both have x so you use product rule
xsiny <--- siny doesn't have x so treat it as coefficient
remember that @hartnn ?
hartnn
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no, product again, because both are functions of x
hartnn
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sin y doesn't have x, right
bu since y is the function of x....
hartnn
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d/dx sin y = cos y dy/dx
DLS
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ive done that only
DLS
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but even WFA treats it as 0
hartnn
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WFA ?
DLS
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wolfaram :P ALPHA
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spelling/*
hartnn
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no...x sin(a+y) needs product rule.
DLS
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:/
hartnn
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x cos(a+y) dy/dx + sin(a+y)
hartnn
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cos y dy/dx =x cos(a+y) dy/dx + sin(a+y)
isolate dy/dx
hartnn
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it doesn't treat it as 0.
DLS
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oh nvm :o
DLS
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but still not clear why product rule..its used in product of 2 functions so x and sin(a+y) x is not a function,y is
hartnn
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x is a function of x
x^1
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doesnt make any sense :S
DLS
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every variable is afunction of itself then
hartnn
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you can say that.
f(x) = x^n with n=1.
DLS
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why didnt we use chain rule for sin(a+y)
hartnn
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we actually did.
DLS
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:o
DLS
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sin is one function and y other right?
hartnn
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cos (a+y) d/dx(a+y)
=cos (a+y) (0+dy/dx)
hartnn
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yes.
DLS
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so I have to treat x&y both as function not variables but other variable like abcd as constants(0) ?
DLS
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when differentiating wrt x
RolyPoly
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\[\frac{d}{dx}xsin(a+y) \]\[=sin(a+y) \frac{d}{dx}(x) + x\frac{d}{dx}sin(a+y)\]\[=sin(a+y) + x[cos(a+y)\frac{d}{dx}(a+y)]\]\[=sin(a+y) + xcos(a+y)\frac{dy}{dx}\]
hartnn
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here since y is the function of x, we treat it as different function.
if a is function of x, then a is also function..... if a is independent of x, then a is constant.
DLS
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clear!
hartnn
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:)