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a) ask student: purpose of differentiation (i), how to perform differentiation (ii) (i) to find the gradient of a curve (ii) multiply the coefficient of x by its indice then minus one from the indici perf...

We want to "undo" every step of the equation until we have just x on one side. So first add 10 to each side and then divide both sides by 2 to give ln(2x+1) = 5. Take the exponential of each sid...

Hint: Use the chain rule

Answer: dy/dx = 4e^(2x+1)

Integrate y=x^2 which is 1/3 x^3 Subsitute the limits, (1/3 (3)^3)-(1/3 (1)^3) 27/3 - 1/3 = 26/3

As why is in the for y=uv where u and v are funtions of x, dy/dx=u'v+v'u (where ' implies the derivative) u=(3x+1)², v=cos(3x) therefore using the chain rule u'=23(3x+1)=18x+6 and v'=-...