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(1) Derivative of a polynomial

The function is given
\( f(x) = -2 x^3 + -5 x^2 + -4 x + -1 \) .
Calculate the first derivative of the function ( f'(x) ).

(2) Derivative of a power function

The function is given
\( f(x) = 5 x^{1} \).
Determine the derivative of the function ( f'(x) ).

(3) Derivative of a root function

The function is given

\( f(x) = 3 \sqrt{x} + 5 x \).
Calculate ( f'(x) ).

(4) Derivative of a rational function

The function is given
\( f(x) = \dfrac{1}{x} + 5 x^2 \).

Determine the derivative ( f'(x) ).

(5) Derivative of an exponential function

The function is given
\( f(x) = 2 e^x + 5 x^2 \).
Calculate the derivative of the function.

(6) Derivative of a trigonometric function

The function is given
( f(x) = 6 \sin x + 1 \cos x ).
Determine ( f'(x) ).

(7) Derivative of a function with a negative exponent

The function is given
\( f(x) = 2 x^{-7} \).
Calculate the derivative.

(8) Derivative by linear combination

The function is given
\( f(x) = 0 x^4 + 3 e^x + 1 \).
Determine ( f'(x) ).

(9) Tangent to the graph of a function

The function is given
\( f(x) = 1 x^2 + 5 x \).
Determine the equation of the tangent line to the graph of the function at the point ( x = 3 ).

(10) Derivative and value of the derivative at a point

The function is given
\( f(x) = 3 x^3 + 0 x \).
Calculate ( f'(x) ) and determine the value at the point ( x = -2 ).

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