d/dx[sin(4x)] = sin(4x) ======
d/dx(x + 2) = d/dx(x) + d/dx(2) = 1 + 0 = 1
I assume you are asking about using differentiation. In this case, where dy-by-dx=0, there is a stationary point on the graph i.e. where the gradient is equal to 0.
Use the "chain rule" of differentiation: y=exp(exp(x)) taking ln both side in y=e x (1/y)dy/dx=e x dy/dx=y*e x dy/dx=exp(x+exp(x))
Calculate dx when xy3 + y = 3x.
There is no single formula for differentiation and anti-differentiation.The deriviative of a function y = f(x) is the limit of delta y over delta x as delta x approaches zero.OR:If f(x)=axn,f'(x)=(an)xn-1The deriviative of 2x3 would be 6x2.The anti-deriviative of a function is the reverse operation, i.e. the function is the deriviative of the anti-deriviative.Anti differentiation introduction:Anti differentiation is also called as integration process. It gives the reverse value of the differentiation equation. Anti differentiation is also called as anti derivative of the function. In this anti differentiation, f(x) is anti derivative of the function F(x). Anti differentiation is used for finding the area of the region under the certain curve. Anti differentiation symbol is denoted as ∫.General formula for anti differentiation:∫ xn dx = [xn + 1 / (n + 1)]+ c∫ k dx = k ∫ dx∫ udv = uv - ∫ v du∫ (w + y) dx = ∫ w dx + ∫ y dxanti-differentiation
d/dx[sin(4x)] = sin(4x) ======
d/dx(x + 2) = d/dx(x) + d/dx(2) = 1 + 0 = 1
I assume you are asking about using differentiation. In this case, where dy-by-dx=0, there is a stationary point on the graph i.e. where the gradient is equal to 0.
Use the "chain rule" of differentiation: y=exp(exp(x)) taking ln both side in y=e x (1/y)dy/dx=e x dy/dx=y*e x dy/dx=exp(x+exp(x))
Calculate dx when xy3 + y = 3x.
x = yy differentiate both sides with respect to x dx = (y * yy-1) dy dy/dx = y * yy-1 dy/dx = yy = x hence differentiate of y wrt x is x only
The definition of the derivative, at a point X = x is the limit, as dx tends to 0, of [f(x+dx)-f(x)]/dx. In this case, therefore, it is lim[3*(x+dx)+2 - (3*x+2)]/dx = lim[3x + 3*dx +2 - 3x - 2]/dx = lim[3*dx/dx] = lim[3] = 3.
Differentiation of the function would give you an instantaneous rate of change at one point; the tangent line. Repeated differentiation of some functions would give you many such points. f(x) = X3 = d/dx( X3) = 3X2 =======graph and see
dx dx dx dx dx dx dx dx dx dx dx dx dx dx dx dx dx d dx dx dx dx dx dx dx dx
by implicit differentiation you have y+x*dy/dx-2dy/dx=0 solving for dy/dx you'll have dy/dx=y/(2-x) and solving for y in the original equation and plugging it back in, you'll get dy/dx=1/(-x^2 +4x-4) which is your final answer
d/dx 2x2+3x+7=4x+3