Answer to Question #315255 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- _____x^1/4 - 12x

3.f(x)= ____ $\sqrt[4]{x}$ ³ - $\xlongequal{}$

4.f (x) = $\xlongequal{}$ - _____x² + $\sqrt[4]{x}$

 

Answer 1

1. $f(x)=-4x⁵+2x^{-4}-2468$

$f'(x)=-20x⁴-8x^{-5}$

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

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

3. $f(x)=4x^{\frac{3}{4}}$

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

4. $f(x)=-2x²+x^{\frac{1}{4}}$

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