Answer to Question #317105 in Calculus 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)= ____ $\sqrt[4]{x}$ $\sqrt[4]{x^3} - \underset{x^6} + \frac{2}{3} x^6$

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

Answer 1

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

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

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