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Find the gradient at x=1 for the curve y=2x*e^2x

The answer to this question is in two parts. We firstly must find the derivative of the function y=f(x) with respect to x, and then substitute the value of x given in the question to find the gradient at ...

Answered by Dominic D. • Maths tutor

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Differentiate y=3xe^{3x^2}+2x

We differentiate y with respect to x:Firstly, we apply the Chain rule in the fist part of the RHS. Remembering the chain rule is uv -> u'v+uv', so d(3xe^{3x^2})/dx=3e^{3x^2}+18x^{2}e^{3x^2}now, we sim...

Answered by John A Alejandro B. • Maths tutor

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A particle of mass 0.5 kg is moving down a rough slope (with coefficient of friction = 0.2) inclined at 30 degrees to the horizontal. Find the acceleration of the particle. Use g = 9.8 ms^-2.

Resolving perpendicular to the plane: R - mg cos30 = 0. Therefore, R = m g cos30, where R is the reaction force perpendicular to the plane. Res...

Answered by Matthew B. • Maths tutor

5986 Views

Evaluate f'(1) for the function f(x) = (x^2 + 2)^5

First, we must differentiate the function. To do this we must let the contents of the bracket be equal to 'u'. We now can produce two equations, one by subbing in 'u' into the function f(x) to give us u^5...

Answered by Tahrim U. • Maths tutor

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You have a five-litres jug, a three-litres jug, and unlimited supply of water. How would you come up with exactly four litres of water (with no measuring cup)?

You fill the 5-litres jug, and pour it into the 3-litres jug until it's full (now you have 2 litres in the 5-litres jug). Then, you pour out the 3-litres jug completely. Now, you pour the 2 litres from th...

Answered by Diana G. • Maths tutor

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