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Read the word problem more than once to make sure you fully understand what is being asked and write down the variables involved. Then try to write down all the derivatives in terms of each other, using t...

y = 2 ^ x

take ln of both sides

ln( y) = ln (2 ^ x)

using the log rules we can bring the power of x down in front of the ln

ln( y ) = x*ln(2)

differentiate both sides wr...

To find the distance between the points A and C, we want to find the magnitude of the vector AC. In order to do this, we must first find the vector AC, which we do by using their position vectors. We are ...

first we need to work out the gradient of the tangent at (5,8). so first differentiate the equation once with respect to x. this gives is dy/dx=2x-4. so at (5,8) the gradient of the tangent is 6. this mea...

23 - 2^0.5