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differentiate (1+2x^2)^(1/2)

This differentiation requires use of the chain rule. The first step is to differentiate the whole thing, treating the bracket as u, so u=1+2x². Therefore we are differentiating u^1/2....

Answered by Reuben S. • Maths tutor

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Find the perpendicular bisector passing through the stationary point of the curve y=x^2+2x-7.

First thing to do is to find the stationary point of the curve. This is done by differentiating the function and then equating to zero, as the gradient of the stationary point is zero. Setting dy/dx to ze...

Answered by Chris M. • Maths tutor

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Solve the following equation: 4(sinx)^2+8cosx-7=0 in the interval 0=<x=<360 degrees.

We first use the identity sin²x+cos²x=1 to substitute for sin^2 in terms of cos.

sin^2(x)=1-cos^2(x) -------------> -4cos^2(x)+8cosx-3=0

Answered by Natalia W. • Maths tutor

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How do you show that (x+2) is a factor of f(x) = x^3 - 19x - 30, and then factorise f(x) completely?

A1) Showing that (x+2) is a factor of f(x). General Method: If A is a number, then (x- A) is a factor of f(x) if when x=A, f(x=A)=0 <-- This is what we want to show ...

Answered by Rebecca W. • Maths tutor

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f(x) = 2x^3 – 7x^2 + 4x + 4 (a) Use the factor theorem to show that (x – 2) is a factor of f(x). (2) (b) Factorise f(x) completely.

We are presented with a third order polynomial with 4 terms, so we expect 3 solutions for f(x)=0. To prove that (x-2) is a factor we must insert the value of x=2 into the function and if f(2)=0 then we ha...

Answered by Nazar A. • Maths tutor

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