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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...

To solve this integral you should use the integration by parts formula, which is uv - integral of vu'. First let x^2 be u, therefore u'(the differential of x^2) = 2x, v' = e^x and therefore v (integral of...