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Find the derivative of e^3x

You keep e 3x and times it by the derivative of the power so 3e 3x .
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Differentiate and then integrate: x^2 + 3x

To differentiate, the rule is to bring the power down to the front and multiply the expression, then take one off the value of the power, for example: d/dx(x 2 ) = (2)x 2-1 = 2x, so the answer to the the que...
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Find the turning point(s) of the following function f(x) = x^2-2x+4. Determine whether the turning point is a minimum or maximum.

Differentiate f(x) with respect to x.You get f'(x) = 2x - 2Turning points occur when the derivative of f(x) = 0. In other words, when f'(x) = 0. This occurs when x=1.Now to determine if maximum or minimum, f...
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Find the equation of the straight line perpendicular to 3x+5y+6=0 that passes through (3,4)

First we need to write the equation in the form y = mx + c 3x + 6= 5y (3x+6) / 5 = y -3/5x + 6/5 = ynow we know that the gradient is -3/5 therefore the perpendicular gradient is 5/3.so our line equation is 5...
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Find the equation of the tangent to the circle (x-3)^2 + (y-4)^2 = 13 that passes through the point (1,7)

Start with a sketch. We can see that the radius from the point (1,7) to the centre of the circle (3,4) is perpendicular to the tangent. The gradient of the radius is (4-7)/(3-1) = -3/2. We know that two perp...
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