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So here we need to use the chain rule in order to differentiate the equation. To start you take the function inside the bracket x²+4x and differentiate it to Du/Dx= 2x + 4 this is known as u. d...

average speed=total distance/time taken ; distance=speed x timeFor the first part of her motion the distance she travelled, d₁=40 x 1/2 (as 30 minutes represent half an hour), so d₁=...

Draw out what the question says. Geometric problems are easier to solve when they can be visualised. First calculate the area of the quarter circle: A = 1/4 \pi r^2Use Pythagoras to calculate the base len...

2sin^2(x) + 3sin(x) = 2cos(2x) + 32sin^2(x) + 3sin(x) = 2(cos^2(x) - sin^2(x) ) + 32sin^2(x) + 3sin(x) = 2(1- 2sin^2(x) ) + 32sin^2(x) + 3sin(x) = 2 - 4sin^2(x) + 36sin^2(x) + 3sin(x) - 5 = 0 let sin(x) =...

a) Sub x=3 into the given equation. N is found to be 25.b) Finding dy/dx gives me, as the first differential is the gradient.First differentiate the power and then multiply the differential of the express...