Derivative

9000070809

Level:

Differentiate the following function.

f (x) = 3 x^{2} \sin x

f^{'} (x) = 6 x \sin x + 3 x^{2} \cos x; x \in R

f^{'} (x) = 6 x \cos x; x \in R

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

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

Level:

Differentiate the following function.

f (x) = \log_{5} 12

f^{'} (x) = 0; x \in R

f^{'} (x) = \frac{1}{\ln 12}; x \in R

f^{'} (x) = \frac{1}{12 \ln 5}; x \in R

f^{'} (x) = 1; x \in R

Level:

Differentiate the following function.

f (x) = \frac{π}{x} + \ln 2

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

f^{'} (x) = 0; x \in R ∖ {0}

f^{'} (x) = π; x \in R ∖ {0}

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

Level:

Differentiate the following function.

f (x) = 3 - 2 \cos x

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

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

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

f^{'} (x) = 2 \cos x; x \in R

Level:

Differentiate the following function.

f (x) = (2 x - 5)^{- 6}

f^{'} (x) = - \frac{12}{(2 x - 5)^{7}}; x \in R ∖ {\frac{5}{2}}

f^{'} (x) = - \frac{12}{(2 x - 5)^{7}}; x \in R

f^{'} (x) = - \frac{12}{(2 x - 5)^{5}}; x \in R ∖ {\frac{5}{2}}

f^{'} (x) = - \frac{12}{(2 x - 5)^{5}}; x \in (\frac{5}{2}; \infty)

Level:

Differentiate the following function.

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

f^{'} (x) = \frac{4 x + 5}{2 x^{2} + 5 x}; x \in (- \infty; - \frac{5}{2}) \cup (0; \infty)

f^{'} (x) = \frac{4 x + 5}{2 x^{2} + 5 x}; x \in R ∖ {- \frac{5}{2}; 0}

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

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

Level:

Differentiate the following function.

f (x) = (x^{2} - 3 x + 2)^{\frac{1}{2}}

f^{'} (x) = \frac{2 x - 3}{2 \sqrt{x^{2} - 3 x + 2}}; x \in R ∖ [1; 2]

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

f^{'} (x) = (4 x - 6) \sqrt{x^{2} - 3 x + 2}; x \in R ∖ [1; 2]

f^{'} (x) = (4 x - 6) \sqrt{x^{2} - 3 x + 2}; x \in R ∖ (1; 2)

Level:

Differentiate the following function.

f (x) = \ln (\frac{1 + x}{1 - x})

f^{'} (x) = \frac{2}{1 - x^{2}}; x \in (- 1; 1)

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

f^{'} (x) = \frac{1 - x}{1 + x}; x \in (- 1; 1)

f^{'} (x) = \frac{1 - x}{1 + x}; x \in R ∖ {- 1; 1}

Level:

Differentiate the following function.

f (x) = \sqrt{\sin x - \cos x}

f^{'} (x) = \frac{\sin x + \cos x}{2 \sqrt{\sin x - \cos x}}; x \in (\frac{π}{4} + 2 k π; \frac{5 π}{4} + 2 k π), k \in Z

f^{'} (x) = \frac{\sin x + \cos x}{2 \sqrt{\sin x - \cos x}}; x \in [\frac{π}{4} + 2 k π; \frac{5 π}{4} + 2 k π], k \in Z

f^{'} (x) = \frac{\sin x - \cos x}{2 \sqrt{\sin x - \cos x}}; x \in [\frac{π}{4} + 2 k π; \frac{5 π}{4} + 2 k π], k \in Z

f^{'} (x) = \frac{\sin x - \cos x}{2 \sqrt{\sin x - \cos x}}; x \in (\frac{π}{4} + 2 k π; \frac{5 π}{4} + 2 k π), k \in Z

Level:

Differentiate the following function.

f (x) = (3 x^{2} + 2)^{3}

f^{'} (x) = 18 x (3 x^{2} + 2)^{2}, x \in R

f^{'} (x) = 18 x (3 x^{2} + 2), x \in R

f^{'} (x) = 18 x^{2} (3 x + 2)^{2}, x \in R

f^{'} (x) = 108 x^{2}, x \in R