Find f\'(x) for f(x) = (2x + 3)(5x^2 + 3x - 4). Find f\'(x) for f(x) = 2x-5/5x +
ID: 2892091 • Letter: F
Question
Find f'(x) for f(x) = (2x + 3)(5x^2 + 3x - 4). Find f'(x) for f(x) = 2x-5/5x + 3. Find f'(x) for f(x) = sin^5(3x^2). Find f'(x) for f(x) = (x^2 + 3) cos 5x. Use implicit differentiation to find the derivative: 3x^2 y^2 + sin (y^2) = x Find y' for y = ln(5x^3 + x^2 -2x + 8). Find y' for y = x^2 e^-5x. Find y' for y = sin(x62) ln(4x). Find y' for y = cos^-1 (x^2). Find y" for y = 8/x. Use logarithmic differentiation to find the derivative of: y = (5 A stone dropped into a still pond sends out a circular ripple increases at a constant rate of 5 ft/min. How rapidly is the by the ripple increasing at the end of 3 min.Explanation / Answer
1) f(x)=(2x+3)(5x^2+3x-4)
f'(x)=(2x+3)(10x+3)+(5x^2+3x-4)(2) =20x^2+6x+30x+9+10x^2+6x-8 =30x^2+42x+1
f'(x)=30x^2+42x+1
2) f(x)=(2x-5)/(5x+3)
differentiating by using quotient rule d(u/v)/dx=[v(du/dx)-u(dv/dx)]/v^2
f'(x)=[(5x+3)*2-(2x-5)*5]/(5x+3)^2 =[10x+6-10x+25]/(5x+3)^2 =31/(5x+3)^2
f'(x) =31/(5x+3)^2
3) f(x)=sin5(3x^2)
f'(x)=5sin4(3x^2)*cos(3x^2)*6x
f'(x)=30x*sin4(3x^2)*cos(3x^2)
4) f(x)=(x^2+3)cos5x
f'(x)=(x^2+3)*(-sin5x)*5+cos5x*2x
f'(x)=(5x^2+15)*(-sin5x)+2x*cos5x
5) 3x2y2+sin(y2)-x=0
differentiating with respect to x
3[x22y(dy/dx)+6xy2]+cos(y^2)*2y(dy/dx) -1=0
dy/dx[6x2y+2ycos(y^2)]+18xy^2-1=0
dy/dx[6x2y+2ycos(y^2)]=1-18xy^2
dy/dx =(1-18xy^2)/(6x2y+2ycos(y^2))
6) y=ln(5x^3+x^2-2x+8)
dy/dx =[1/(5x^3+x^2-2x+8)]*(15x^2+2x-2)
dy/dx =[(15x^2+2x-2) /(5x^3+x^2-2x+8)]
7) y=x2e(-5x)
dy/dx=x2(-5*e(-5x))+2xe(-5x)
dy/dx=-5x2e(-5x)+2xe(-5x)
8) y=sin(x^2)ln(4x)
dy/dx =sin(x^2)*(4/(4x))+ln(4x)*cos(x^2)*2x
dy/dx =(1/x)*sin(x^2)+(2x)*ln(4x)*cos(x^2)
9) y=arccos(x^2)
dy/dx =[-1/sqrt(1-(x^2)^2)] *(2x)
dy/dx =(-2x)/sqrt(1-x^4)
10) y=8/x
we can write y as
y=8x-1
y' =(-1)*8x-2
y''=(-1)*8*(-2)*x-3
y''=16/x3
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