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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]

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/dx = (v (...

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 write u = x^...

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

To find the inverse of a function you need to rearrange from y= a function in terms of x to x= a function in terms of y and then when you write your answer it's important to set it in the form f^-1(x)= a fun...