Answer to Question #317800 in Calculus for Niu_bi

Question #317800

ACTIVITY IN BASIC CALCULUS

BASIC RULES IN DERIVATIVE


 Complete the blanks of the given function below with a number (except 0 and 1) to create your own problem and find the derivative of the function. Show your complete solution to each problem.

 

1. f(x) = -4x5+ ______x-4 - 2468


2. f (x) =____x-3- _____x1/4 - 12x


3.f(x)= ____ "\\sqrt[4]{x^3} - \\underset{x^6}{=} + \\frac{2}{3} x^6"


4.f (x) = "\\underset{x^-6}{=} -" ____ x2 + "\\sqrt[4]{x}"


1
Expert's answer
2022-03-25T15:27:52-0400


1. f(x) = -4x5+ ______x-4 - 2468 "f(x)=-4x^5+3x^{-4}-2468"

"f'(x)=(5\\times-4)x^{5-1}+(-4\\times3)x^{-4-1}-0"



"=-20x^4-12x^{-5}"



2. f (x) =____x-3- _____x1/4 - 12x

"f{x}=2x^{-3}-4x^{\\frac{1}{4}}-12x"

"f'(x)=(-3\\times2)x^{-3-1}-(\\frac{1}{4}\\times4)x^{\\frac{1}{4}-1}-12x^{1-1}"



"=-6x^{-4}-x^{-\\frac{3}{4}}-12"



3.f(x)= ____ "\\sqrt[4]{x}" "\\sqrt[4]{x^3} - \\underset{x^6} + \\frac{2}{3} x^6"


"f(x)=5x-x^6+\\frac{2}{3}x^6"



"f'(x)=5-6x^5+4x^5 =5-2x^5"



4.f (x) = "\\underset{x^-6}{=} -" ____ x"\\sqrt[4]{x}"

"f(x)=x^{-6}-7x^2+x^{\\frac{1}{4}}"



"f'(x)=-6x^{-7}-14x+\\frac{1}{4}x^{-\\frac{3}{4}}"




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