How do you find the second derivative of #y=Asin(Bx)#?
#(d^2y)/dx^2 = AB^2sin(Bx)#
We use
Making a distinction:
once provides us with:
Redifferentiating, we obtain:
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To find the second derivative of ( y = A\sin(Bx) ), where ( A ) and ( B ) are constants:

Find the first derivative of ( y ) with respect to ( x ): [ y' = AB\cos(Bx) ]

Find the second derivative of ( y' ) with respect to ( x ): [ y'' = AB^2\sin(Bx) ]
So, the second derivative of ( y = A\sin(Bx) ) is ( y'' = AB^2\sin(Bx) ).
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To find the second derivative of ( y = A \sin(Bx) ), where ( A ) and ( B ) are constants, you first find the first derivative using the chain rule, which states that the derivative of ( \sin(u) ) is ( \cos(u) ) times the derivative of ( u ). Applying this rule, the first derivative of ( y ) is:
[ \frac{dy}{dx} = AB \cos(Bx) ]
To find the second derivative, you differentiate ( \frac{dy}{dx} ) with respect to ( x ) again:
[ \frac{d^2y}{dx^2} = \frac{d}{dx} \left( AB \cos(Bx) \right) ]
Using the chain rule again, this becomes:
[ \frac{d^2y}{dx^2} = AB^2 \sin(Bx) ]
So, the second derivative of ( y = A \sin(Bx) ) is ( AB^2 \sin(Bx) ).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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