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What is the derivative of y=(e^(2x))(sin(3x))

This question is slightly complex and requires you to use multiple differentiation rules. Since we are differentiating a product of two functions, the first rule that we have to use is the product rule: mult...
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Answered by Sajidah H. • Maths tutor
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Differentiate y= exp(cos^2(x)+sin^2(x)) by using the chain rule.

First of all instead ,we'll define the chain rule , thus y can be rewritten as y = f (g(x)) , where f(x) = exp (x) and g(x) = cos^2(x) + sin^2(x). Therefore let y = f(u) , dy/dx = dy/du * du/dx , which then ...
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Answered by Ayman J. • Maths tutor
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The point P lies on a curve with equation: x=(4y-sin2y)^2. (i) Given P has coordinates (x, pi/2) find x. (ii) The tangent to the curve at P cuts the y-axis at the point A. Use calculus to find the coordinates of the point A.

To find the x coordinate of point P, we simply substitute in the value of y at P into the equation of the curve and solve for x = 4pi^2. (ii) To start, we can differentiate x with respect to y, by using the ...
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Answered by Tobias F. • Maths tutor
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The point P lies on the curve C: y=f(x) where f(x)=x^3-2x^2+6x-12 and has x coordinate 1. Find the equation of the line normal to C which passes through P.

First we must find the y coordinate of the point P: We know the x-coordinate is x1=1 so the y coordinate must satisfy the equation y1=f(1) which gives y1=-7. So we now know P is at (1,-7). We now need to fin...
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Answered by Kieran H. • Maths tutor
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Express square root of 48 in the form n x square root of 3 , where n is an integer

We know that 3 x 16 = 48 This is equivalent to saying 3 x 4^2 = 48 Therefore the square root of 48 can be written as square root of (4^2 x 3) = 4 x square root 3
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Answered by Helena W. • Maths tutor
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