Answer to Question #315535 in Differential Equations for Niu_bi

Question

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 + $\sqrt[4]{x}$

Answer 1

1.$f(x)=-4x^5+2x^{-4}-2468$

$f'(x)=-20x^4-8x^{-5}-2468$

2.$f(x)=3x^{-3}-4x^{1/4}-12x$

$f'(x)=-9x^{-4}-x^{-3/4}-12$

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

$f'(x)=3x^{-1/4}-6x^5+4x^5$

4. $f(x)=x^{-6}-2x^2+\sqrt[4]{x}$

$f'(x)=-6x-4x+\frac{1}{4}x^{-3/4}$