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To get the required tangent equation we need its gradient and the coordinates of a point it passes through. We can then substitute it into the formula y - y 1 = m(x - x 1 ). 1. Finding the gradient: To find ...

You use integration by parts if there's more than one function of x. For example; to integrate x sin(x) you'd use integration by parts as this is two functions of x. The formula to remember is I(udv) = uv - ...

Using integration by parts, by substituting ln(3x) as u and x^8 as dv/dx, use the formula to plug in the values and complete the calculation to get (x^9)(ln(3x)-1/9)/9

We can see that we have the product of two different functions, and so we need to use the product rule. We will separate the function and label each part u and v for clarity. So we let u = 2e x and let v = s...

First, we must rearrange to give 2tan(θ) = 5x. Differentiate both sides with respect to x: 2sec 2 (θ)dθ/dx = 5 Use identity sin 2 (θ) + cos 2 (θ) = 1, dividing through by cos 2 (θ), to get 2(1+tan 2 (θ))dθ/d...