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Find the integral of 1/(x-5) with respect to x

This question tests fundamental understanding of integration and checks that the student is not simply memorizing the simple examples for the test. Most students will remember that the integral of 1/x is ln(...
HL
Answered by Harry L. • Maths tutor
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y = x^x, find y'

y = x x , by taking logs:ln(y) = ln(x x )By log laws:ln(y) = xln(x)From implicit differentiation; d/dx = y'*d/dy, so:d/dx[ln(y)] = y'*d/dy[ln(y)] = y' * 1/yFrom the product rule; d/dx[xln(x)] = ln(x) * d/dx(...
SD
Answered by Scott D. • Maths tutor
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Find the equation of the tangent to the curve y = 3x^2 + 4 at x = 2 in the form y = mx + c

There are two main steps. First find the gradient of the curve at x = 2 (m). This is done by differentiating the curve equation y = 3x^2 + 4 to get dy/dx = 6x. By plugging in x = 2, we get the gradient of th...
Answered by • Maths tutor
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A cannonball is fired at an angle of 30 degrees and a velocity of 16 m/s. How long does it take (to 2 significant figures) for the cannonball to reach the ground?

First, we make the standard assumption that there is no air resistance, meaning that gravity is the only force acting on our cannonball. We then use the SUVAT equations, so: S = 0m (because it will return to...
NB
Answered by Nada B. • Maths tutor
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The curve C has equation ye^(-2x) = 2x + y^2. Find dy/dx in terms of x and y.

The curve's equation is presented as an implicit function. Therefore we must use implicit differentiation to solve this problem. To do this, we differentiate both sides of the equation with respect to x, app...
GW
Answered by Georgia W. • Maths tutor
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