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How can I find the derivative of y = tan(x)?

Let's first recall the definition of tan(x) = sin(x)/cos(x). Hence, y' = d/dx( sin(x)/cos(x) ). Recall quotient rule for differentiation: ( f(x)/g(x) )' = ( f '(x)^2*g(x) - f(x)*g'(x)^2 ) / g(x)^2 and that d...
RB
Answered by Riccardo B. • Maths tutor
6198 Views

Solve the following equations x^2-2x+4=0, x^2+4x+1=0

x 2 -2x+4= (x-2)(x-2)=0 x=-2 (double root) x 2 +5x+1=0 x 1,2 = -5+_ (5 2 -4(1)(1) ) 0.5 /2 x 1 =4.8 x 2 =-0.2 (to 1 d.p.)
KF
Answered by Kyriakos F. • Maths tutor
3778 Views

y = 4x / (x^2 + 5). Find dy/dx.

We use the quotient rule here which states that if y = f(x)/g(x) then dy/dx = (f'(x)g(x) - g'(x)f(x)) / (g(x)^2). Here f(x) = 4x and g(x) = x^2 + 5, so we have f'(x) = 4 , g'(x) = 2x. This gives us dy/dx = (...
PS
Answered by Patrick S. • Maths tutor
11275 Views

Find the values of k for which the equation (2k-3)x^2-kx+(k-1) has equal roots

We know that an equation has equal roots if the sqrt(b^2-4ac) term in the quadratic equation is equal to zero. Therefore using this information we can form an expression for k to be (-k)^2-4(2k-3)(k-1)=0. Fr...
EH
Answered by Eliott H. • Maths tutor
13879 Views

Earth is being added to a pile so that, when the height of the pile is h metres, its volume is V cubic metres, where V = (h6 + 16) 1 2 − 4.Find the value of dV/dh when h = 2.

As V=(h 6 +16) 1/2 -4 , the chain rule can be used to calculate dV/dh. dV/dh=3h 5 (h 6 +16) -1/2 h=2 can be substituted in to find the solution. 3 2 5 (2 6 +16) -1/2 =10.73
LK
Answered by Lewis K. • Maths tutor
6751 Views