Derivative Help(Calculus)

The derivative by definition lim?x?0fx+?x-fx?x drive: fx=x2 fx+?x-fx?x (x+?x)2-x2?x x2+2x?x+?x2-x2?x The x2 cancel come in because on is + and the other is - 2x?x+(?x)2?x ?x2x+?x?x set up the equation. The ?x will cancel out because you are dividing the homogeneous thing. 2x+?x 2x in the answer because ?x will go to 0 which leaves 2x. first derivative of a product y=gx?hx Or y=u?v dydx=udvdx+vdudx Example: ddx4x+37x-1 dydx=udvdx+vdudx 4x+3dvdx7x-1+7x-1dudx4x+3 4x+37+7x-1(4) multiply the 7 into the 4x+3 and the 4 into the 7x-1. 28x+21+28x-4 match or set forth like terms. 56x+17 in the answer. differential of a quotient y=g(x)h(x) Or y=uv ddxuv=vdudx-udvdxv2 Example: ddx5x+34x2-7 ddxuv=vdudx-udvdxv2 4x2-7dudx5x+3-5x+3dvdx4x2-74x2-72 4x2-75-5x+38x4x2-72 multiply the 5 into the 4x2-7 and the 8x into the 5x+3. 20x2-35-40x2-24x4x2-72 add or subtract like terms. -20x2-24x-354x2-72 is the answer. The De rivative of a power dydx=ddxun=nun-1dudx Example: y=3x+250 dydx=ddx3x+250 503x+250-1ddx(3x-2) 503x+249(3) multiply the 3 and 50 150(3x+2)49 is the answer The chain rule dydx=dydx?dudx Example: y=3x2+5 dydx=ddx3x2+5 ddx3x2+512 123x2+512-1ddx3(2)x2-1+5 123x2+5-126x multiply 6x into 12.

3x3x2+5 is the answer inseparable Differentiation Example: dydx if 2y3+3x2y-8x3+2x-y=dydx0 23y3-1+3x2y1-1+y32x2-1-83x3-1+21x1-1-y1-1dydx=0 6y2+3x2+6xy-24x2+2-1dydx=0 6y2+3x2-1dydx=-6xy+24x2-2 dydx=-6xy+24x2-26y2+3x2-1 Velocity: v=dsdt (s is the rate change and t is the time) Acceleration: a=dvdt=d2sdt2 Derivative of transcendental functions ddx(sinu)= cosududx ddxcosu=-sinududx ddxtanu=sec2u! dudx ddxcotu=-csc2ududx ddxsecu=secutanududx ddxcscu=-cscucotududx Inverse trigonometric functions ddxacrsin u=11-u2dudx ddxarccosu=-11-u2dudx ddxarctanu=11+u2dudx ddxarccotu=-11+u2dudx ddxarcsecu=1u2u2-1dudx ddxarccscu=-1u2u2-1dudx Laws of exponents am?an=am+n...If you want to get a full es judge, say it on our website: OrderEssay.net

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