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Differentiate with respect to x: (6x + 7)e^x

Product Rule: dy/dx (uv) = u'v + uv'
Let u = 6x+7 and v = e^x. Using simple disintegartion, u' is 6 and v' is e^x.
Therefore, answer is: 6e^x + (6x +7)e^x

Answered by Aisha R. • Maths tutor

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How do I integrate cos^2x with respect to x?

This can be a very tricky question if you do not know how to approach it. Our first instinct may be to try a substitution, but this gets us nowhere. In fact, the trick is to make use of the identity

Answered by Raiad S. • Maths tutor

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Point P on the curve, x = 2tan( y+ π/12), has a y-coordinate of π/4. Find an equation for the normal to the curve at P.

Step 1 - Firstly, we need to find the x-coordinate of point P. This will allow us to find the normal equation required in the question. To find the x-coordinate, we plug in the value of y given in the que...

Answered by Andrew M. • Maths tutor

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Integrate sin^2(x)

sin^2(x) is not one of the functions whose antiderivative is commonly known to us. When we see trigonometric functions our best bet is usually to think of some trigonometric identity we know. In this case...

Answered by John P. • Maths tutor

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A circle with center C has equation x^2 + y^2 + 8x - 12y = 12

Circle equation = (x - a)²+ (y - b)² = r²Where Centre coordinates (a, b) and radius 'r'Therefore x² + y² + 8x - 12y = 12 is to be rewritten in this ...

Answered by Henry K. • Maths tutor

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