Answer to Question #315539 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

$1.f(x)=−4x ^5+2x ^{ −4} −2468$

$f′ (x)=−20x^4−8x^{−5}$

2. $f(x)=3x ^{ −3} −4x ^{ 1/4} −12x$

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

3. $f(x)=4x^{3/4}-x^6+2/3x^6$

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

$4.f(x)=x^{-6}-2x^2+x^{1/4}$

$f'(x)=-6x^{-7}-2x+1/4x^{-3/4}$