Question
Rewrite the parametric equations
y=3(x−5)
Evaluate
{x=5+ty=3t
Choose the parametric equation
x=5+t
Solve the equation
t=x−5
Solution
y=3(x−5)
Show Solution
Find the first derivative
dxdy=3
Evaluate
{x=5+ty=3t
To find the derivative dxdy,first find dtdx and dtdy
dtd(x)=dtd(5+t)dtd(y)=dtd(3t)
Find the derivative
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Evaluate
dtd(x)=dtd(5+t)
Calculate the derivative
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Evaluate
dtd(x)
Use differentiation rules
dxd(x)×dtdx
Use dxdxn=nxn−1 to find derivative
dtdx
dtdx=dtd(5+t)
Calculate the derivative
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Evaluate
dtd(5+t)
Use differentiation rule dxd(f(x)±g(x))=dxd(f(x))±dxd(g(x))
dtd(5)+dtd(t)
Use dxd(c)=0 to find derivative
0+dtd(t)
Use dxdxn=nxn−1 to find derivative
0+1
Removing 0 doesn't change the value,so remove it from the expression
1
dtdx=1
dtdx=1dtd(y)=dtd(3t)
Find the derivative
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Evaluate
dtd(y)=dtd(3t)
Calculate the derivative
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Evaluate
dtd(y)
Use differentiation rules
dyd(y)×dtdy
Use dxdxn=nxn−1 to find derivative
dtdy
dtdy=dtd(3t)
Calculate the derivative
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Evaluate
dtd(3t)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
3×dtd(t)
Use dxdxn=nxn−1 to find derivative
3×1
Any expression multiplied by 1 remains the same
3
dtdy=3
dtdx=1dtdy=3
Solution
dxdy=3
Show Solution