Derivatives - Chain, Implicit, Inverse Trig

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Find: f'(x) =

• 9x^-1/3

• -3x^-4/3

• -9x^2/3

• -3x^2/3

Find  $\frac{d^2y^{ }}{dx^2}$  by Implicit Differentiation 
 $x^3+y^3=36$  

•  $\frac{-x^2}{y^2}$  

•  $\frac{-2xy^2+2xy}{y^2}$  

•  $\frac{-2xy^3-2x^4}{y^5}$  

•  $\frac{-2xy^2-2x^4}{y^4}$  

Find dy/dx by Implicit Differentiation

x + 4y = 1

• -1/4

• -1

• 4

• 1

• A

• B

• C

• D

Find y' if y = tan(3x²+2).

• sec²(3x²+2)

• 6xsec²(3x²+2)

• 6xsec²x(3x²+2)

• sec²(6x)

Find the derivative:

y=log₉x

• y′=1 /((log9)x)

• y′=(ln9)/x

• y′=1/(x(lnx))

• y′=1/((ln9)x)

Find the derivative:

y=(2^3x+4)

• 3(ln2)(2^3x+4)

• 3(2^3x+4)

• 3(2^3x+4/(ln2))

• 2^3x+4

Find the derivative f(x) = xe^x

• f'(x) = e^x

• f'(x) = xe^x + xe^x

• f'(x) = e^x - xe^x

• f'(x) = e^x + xe^x

Find the derivative:

y=log₄(6x+5))

• (ln4)(1/(6x+5))

• (6ln4)/(6x+5)

• 6/((ln4)(6x+5))

• 6/(6x+5)