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First, straight away from reading the question you know this question will involve differentiating the function with respect to x so immediately you want to re-write the equation in terms of y which in th...

u = ln (x+1) v = sin x
du/dx = 1/(x+1) dv/dx = cos x
Therefore, by the product rule,
dy/dx = [sin x / x+1] + [ln (x+1) cos x]

1. To find the gradient of the curve we must differentiate the function. The function is in the form of a quotient, y=u/v, where u and v are functions of x. Therefore, we can use the quotient rule, dy/...

1. Firstly, we must recognise that the function is in the form of a product, y=uv, where u and v are functions of x. Therefore, we can use the product rule, dy/dx = u (dv/dx) + v (du/dx). 2) We can wri...

5x^2 becomes 25x as the 2 comes down and 2x becomes 2 as x becomes 1.dy/dx = 25x + 2=10x+2