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Implicit differentiation involves differentiating expressions for which it is difficult to rearrange into y in terms of x. It is important to note which variable is being differentiated by the other as, f...

For part i) we use the basic method of differentiation by considering each term individually. The first term, x³ goes to 3x² by multiplying the original term by the original power, b...

First you must write the function in terms on something you know how to differentiate, for example... by taking tan (..) of both sides the equation becomes, tan(y)= ax² +b. We then use implicit...

x=2t --> t= x/2 
y=t² = (x/2)². 

So the Cartesian equation is y=x²/4. 

To answer this question we observe that y is the product of x^2 and sin(x), so we use the product rule. Then dy/dx = 2x * sin(x) + cos(x) * x^2 The resulting equation can be tidied up by factoring out x a...