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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...

1/2