Derivative

2110002101

Level:

In one of the following pictures there is a graph of a function, which has null derivative at the point

x = 1

. Choose this picture.

Level:

Differentiate the following function.

f (x) = \ln (\frac{2 x}{2 - x})

f^{'} (x) = \frac{2}{(2 - x) x}; x \in (0; 2)

f^{'} (x) = \frac{2}{(2 - x) x}; x \in R ∖ {0; 2}

f^{'} (x) = \frac{2 - x}{2 x}; x \in (0; 2)

f^{'} (x) = \frac{2 - x}{2 x}; x \in R ∖ {0; 2}

Level:

Differentiate the following function.

f (x) = \ln (3 x^{2} - 5 x)

f^{'} (x) = \frac{6 x - 5}{3 x^{2} - 5 x}; x \in (- \infty; 0) \cup (\frac{5}{3}; \infty)

f^{'} (x) = \frac{6 x - 5}{3 x^{2} - 5 x}; x \in R ∖ {0; \frac{5}{3}}

f^{'} (x) = \frac{1}{3 x^{2} - 5 x}; x \in (- \infty; 0) \cup (\frac{5}{3}; \infty)

f^{'} (x) = \frac{1}{3 x^{2} - 5 x}; x \in R ∖ {0; \frac{5}{3}}

Level:

Differentiate the following function.

f (x) = \frac{\sqrt{x} + 2}{2 - \sqrt{x}}

f^{'} (x) = \frac{2}{\sqrt{x}} \frac{1}{(2 - \sqrt{x})^{2}}, x \in (0; 4) \cup (4; \infty)

f^{'} (x) = \frac{\sqrt{x}}{2 (2 - \sqrt{x})^{2}}, x \in (0; 4) \cup (4; \infty)

f^{'} (x) = \frac{1}{(2 - \sqrt{x})^{2}}, x \in (0; 4) \cup (4; \infty)

f^{'} (x) = \frac{1}{x (2 - \sqrt{x})^{2}}, x \in (0; 4) \cup (4; \infty)

Level:

Differentiate the following function.

f (x) = \frac{2 - x^{2}}{4 x}

f^{'} (x) = \frac{- x^{2} - 2}{4 x^{2}}, x \in R ∖ {0}

f^{'} (x) = \frac{- x}{2}, x \in R ∖ {0}

f^{'} (x) = \frac{2 - x^{2}}{4 x^{2}}, x \in R ∖ {0}

f^{'} (x) = \frac{- x - 2}{4 x^{2}}, x \in R ∖ {0}

Level:

Differentiate the following function.

f (x) = \cos (3 - 2 x^{2})

f^{'} (x) = 4 x \sin (3 - 2 x^{2}), x \in R

f^{'} (x) = - 4 x \sin x, x \in R

f^{'} (x) = - \sin (4 x), x \in R

f^{'} (x) = \cos (4 x + 1), x \in R

Level:

Differentiate the following function.

f (x) = \cos x (1 - cotg x)

f^{'} (x) = - \sin x + \cos x + \frac{\cos x}{\sin^{2} x}, x \in R ∖ {k π; k \in Z}

f^{'} (x) = \frac{\cos x}{\sin^{2} x}, x \in R ∖ {k π; k \in Z}

f^{'} (x) = - \sin x + \cos x, x \in R ∖ {k π; k \in Z}

f^{'} (x) = - \sin x + 2 \cos x, x \in R ∖ {k π; k \in Z}

Level:

Differentiate the following function.

f (x) = e^{x} x^{4}

f^{'} (x) = e^{x} x^{3} (x + 4), x \in R

f^{'} (x) = e^{x} 4 x^{3}, x \in R

f^{'} (x) = e^{x} x^{3} (x - 4), x \in R

f^{'} (x) = e^{x} x^{3} (x + x e^{x}), x \in R

Level:

Differentiate the following function.

f (x) = 3 \cos x - 2

f^{'} (x) = - 3 \sin x; x \in R

f^{'} (x) = - 3 \cos x; x \in R

f^{'} (x) = 3 \sin x - 2; x \in R

f^{'} (x) = - 3 \sin x - 2; x \in R

Level:

Differentiate the following function.

f (x) = π - \frac{\ln 3}{x}

f^{'} (x) = \frac{\ln 3}{x^{2}}; x \in R ∖ {0}

f^{'} (x) = 0; x \in R ∖ {0}

f^{'} (x) = \ln 3; x \in R ∖ {0}

f^{'} (x) = - \frac{\ln 3}{x^{2}}; x \in R ∖ {0}