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theta = arctan(5x/2). Using implicit differentiation, find d theta/dx.

First, we must rearrange to give 2tan(θ) = 5x. Differentiate both sides with respect to x: 2sec 2 (θ)dθ/dx = 5 Use identity sin 2 (θ) + cos 2 (θ) = 1, dividing through by cos 2 (θ), to get 2(1+tan 2 (θ))dθ/d...
CW
Answered by Callum W. • Maths tutor
4648 Views

f(x) = x^3 + 3x^2 + 5. Find f'(x) and f''(x).

With differentitaion you multiply the fatcor it's raised by and minus one from the order e.g. y = x^n so y' = nx^(n-1) So f'(x) = 3x^2 + 6x and f''(x) = 6x + 6
NS
Answered by Nikita S. • Maths tutor
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What is the equation of the tangent to the circle (x-5)^2+(y-3)^2=9 at the points of intersection of the circle with the line 2x-y-1=0

Teh points of intersection can be found by subbing in y=2x-1 to the equation of the circle. (x-5) 2 +(2x-1-3) 2 =5x 2 -26x+33=9 so we have 5x 2 -26x+24=0. Solving the quadratic equation gives x 1 =4 and x 2 ...
TD
Answered by Tutor67416 D. • Maths tutor
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When do I use the product rule as opposed to the chain rule?

The product rule is used when two functions of x are multiplied by each other, hence, product. So this can be used to differnetiatate 3x 2 * x+1 or more complex functions like sinxcosx. The chain rule is use...
LU
Answered by Lota U. • Maths tutor
4339 Views

A line runs between point A(5,9) and B(11,1). Find the equation of the line. Point C lies on the line between A and B. The line with equation 2y=3x+12 also crosses through point C. Find the x coordinate of Point C.

For the first part it would be a good idea to sketch out the graph. Then using the formula 'change in y/change in x' find the gradient of the line (-4/3). You can then either use the formula y=mx+c and put i...
AT
Answered by Amelia T. • Maths tutor
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