SOLUTION: Evening All, Right its been a while since i have attempted maths, and have just gone back to further ed. I have attempted the following questions, which im sure should be simple, b
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Question 366198: Evening All, Right its been a while since i have attempted maths, and have just gone back to further ed. I have attempted the following questions, which im sure should be simple, but of course like anything its just getting back into things after a number of years. i have listed the questions below, and my answers if anybody will take the time to have a quick look and correct me where neccessary i would appreciate this.
1)Find dy/dx by differentiating with respect to x the following expressions.
a) y=x^3-6x^2+9x-1 = 3x^2-12x+8
b) y=1/2x -sqrtx = 1/2-1/2x^-1/2
c) y=e^x-e^-x = e^x+e^-x
d) y=25cosx--sinx = -25sinx-cosx
e) y= 3sinhx-4coshx = 3hsinhx+4hsinhx
f) y= (x^2+1) sinhx = 1
2 Use product rule to obtain dy/dx for the following
a) y=x^2e^x = 2x(e^x)+x^2(e^x)
b) y= xtanx = 1(tanx)+x(sec^2x)
c) y= x^4ln(x)= 4x^3(ln(x))+x^4(1/x)
d) y= x^2sinx = 2x(sinx)+x^2(cosx)
e) y= e^-xcosx = -e^-x(cos x)+ e^-x (-sinx)
f) y=(x^2+1)sinhx = (2x +1) (sinhx)+(x^2+1)(cosh x)
Finally, use the quotient rule to differentiate with respect to x, simplifying as far as possible.
a) y= sinx/1+e^-x = 1+e^-x(cpsx)-(1-e^x)sinx/(1+e^-x)^2
b) y= lnx/1+x^2 = 1+x^2(1/x)-1+2x(ln x)/(1+x^2)^2
Really this would be appreciated thank you
Found 2 solutions by user_dude2008, Fombitz:
Answer by user_dude2008(1862) (Show Source): You can put this solution on YOUR website!
a) =3x^2-12x+9)
b) =\frac{d}{dx}\left(\frac{1}{2}x-x^{\frac{1}{2}} \right)=\frac{1}{2}-\frac{1}{2}x^{-\frac{1}{2}}=\frac{1}{2}-\frac{1}{\sqrt{x}})
c) =e^x-(-e^{-x})=e^{x}+e^{-x}=e^x+\frac{1}{e^x})
d) -\sin(x)\right)=-25\sin(x)-\cos(x))
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
1a)
b) Correct!
c) Correct!
d) Correct!
e)
I think you misinterpreted as when it's actually the hyperbolic sine function, , same for the cosine.
f)
.
.
.
2a) Correct! Could be simplified to
b) Correct!
c) Correct! Could be simplified to
d) Correct!
e) Correct! Could be simplified to
f) Correct! but why weren't your answers for 1f and 2f the same??
.
.
.
3a)
.
b)
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