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junior college 1 | H2 Maths
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Hi!! Can someone please help me with implicit differentiation for these questions? I know it’s basic but i can’t even do the first one because i don’t know if i’m just supposed to multiply d/dx inside :( Thank u so much!!
Date Posted: 4 years ago
Views: 275
First one :
dy/dx means differentiation of y with respect to x, whereby y is a function of x.
i.e y = f(x)
So d/dx (dy/dx) just means to differentiate this with respect to x again
d/dx (dy/dx) = d²y/dx²
This is the second derivative.
Alternative representation :
y = f(x)
dy/dx = d/dx ( f(x) ) or d(f(x))/dx= f'(x)
d/dx (dy/dx) = d/dx ( f'(x) ) or d(f'(x))/dx
= f''(x)
= d²y/dx²
dy/dx means differentiation of y with respect to x, whereby y is a function of x.
i.e y = f(x)
So d/dx (dy/dx) just means to differentiate this with respect to x again
d/dx (dy/dx) = d²y/dx²
This is the second derivative.
Alternative representation :
y = f(x)
dy/dx = d/dx ( f(x) ) or d(f(x))/dx= f'(x)
d/dx (dy/dx) = d/dx ( f'(x) ) or d(f'(x))/dx
= f''(x)
= d²y/dx²
d/dx does not mean multiplying.
It means differentiating with respect to x.
It means differentiating with respect to x.
See 1 Answer
done
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clear
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Hi I have given a helping hand by solving 2 questions. For implicit differentiation if it’s d/dx(dy/dy) you will just get the second order of differentiation so it’s d^2y/dx^2.
Date Posted:
4 years ago
d/dx (dy/dx) rather than d/dx (dy/dy)
Yup a mistake there! Sorry my bad, Thanks!
No worries, just helping
A number of my Sec 4 students think that dy/dx (dy/dx) is no different from d/dx (dy/dx). When they started learning it they did not think that it would actually be different. It’s not that explicitly taught in Sec 4.
It is important to recognise that d/dx is an operator, not a fraction
dy/dx means the operator has been applied on y already. Hence dy/dx (dy/dx)
Is simply (dy/dx)²
Whereas d/dx (dy/dx) is an operation on the first derivative. This leads to the second derivative which is represented by d²y/dx² (also can be seen to be applying the operator twice on y itself).
Teachers should have made this clear in O level teaching.
Is simply (dy/dx)²
Whereas d/dx (dy/dx) is an operation on the first derivative. This leads to the second derivative which is represented by d²y/dx² (also can be seen to be applying the operator twice on y itself).
Teachers should have made this clear in O level teaching.
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