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What is the formula of the chain rule based off the formula d/dx f[g(x)]?
f’[g(x)] x g’(x)
What is the formula of the power rule based off the formula [x^n]?
(n)x^n-1
What is the formula of the quotient rule based off the formula [u/v]?
(v x u’) - (u x v’)/ v^2
What is the formula of the product rule based off the formula [uv]?
(u x v’) + (v x u’)
What is d’(x) of 5x^2-6x^10?
d'(x)=10x-60x^9
What is d’(x) of 6x^2?
d’(x)=12x
What is d’(x) of 3x^2 + 7x^10 - 6x^10?
d'(x)=-50x^9 + 6x (6x + 10x^9 -60x^9)
What is d’(x) of 3^x + 3x^2?
d'(x)=3^ x ln 3 + 6x
What is d’(x) of sec(x) + tan(x)?
d’(x)= sec(x)tan(x) + sec^2(x)
What is d’(x) of cos(sin(x))?
d’(x)= -sin(sinx) x cosx
(*CHAIN RULE)
What is d’(x) of 3/7 cos(x)?
d’(x)= 3/7 -sin x
What is d’(x) of 5/x?
d'(x)=-5x/2
What is dy/dx’(x) of x^3-x^4 when x=4?
dy/dx'(x)= 12
x^3-x^4
3x^2-4x^3
3(4^2)-4(2^3)
3 (16)- 4(8)
48-36=12
What is f’(x) of x^2lnx?
f’(x)=2xlnx+x
What is d’(x) of d(x) of (x^2-5)(x^3-2x+3)?
d’(x)= 5x^4-21x^2+10
(*PRODUCT RULE)
What is d’(x) of ln x?
d'(x)=1/x
You are planning to make an open rectangle box from an 8in. by 11in. piece of graph paper by cutting congruent squares from the corners and folding up the sides. What are the dimensions of the box of the largest volume you can make this way, and what is the volume?
v= 60in^3
Find the second derivative of f(x)= -4x^2 + 5x^5 - 2x^3.
f’(x)= 25x^4-6x^2-8x
f’’(x)=100x^3-12x-8
You are planning to make an open rectangle box from an 8in. by 11in. piece of graph paper by cutting congruent squares from the corners and folding up the sides. What are the dimensions of the box of the largest volume you can make this way, and what is the volume?
dA/dt= 40
Find the second derivative of f(x)= =2x^2-8x-9.
f’(x)= -4x-8
f’’(x)=-4