Question

ОЧЕНЬ СРОЧНО ПОЖАЛУЙСТА 20 ВАРИАНТ СРОЧНО!!!!! ​

Answer 1

Ответ:

1

$f'(x) = 5 \times 6 {x}^{5} - 8 + 0 = 30 {x}^{5} - 8$

2

$f(x) = \frac{3 }{ {x}^{8} } - \frac{ {x}^{9} }{3} + 6 \sqrt{x} = \\ = 3 {x}^{ - 8} - \frac{ {x}^{9} }{3} + 6 {x}^{ \frac{1}{2} }$

$f'(x) = 3 \times ( - 8) {x}^{ - 9} - \frac{1}{3} \times 9 {x}^{8} + 6 \times \frac{1}{2} {x}^{ - \frac{1}{2} } = \\ = - \frac{24}{ {x}^{9} } - 3 {x}^{8} + \frac{3}{ \sqrt{x} }$

3

$f'(x) = (tgx)'(x - 4) + ( x - 4)' \times tgx = \\ = \frac{x - 4}{ \cos {}^{2} (x) } + tgx$

4

$f(x) = \frac{ {x}^{6} - 1} { \sin(x) }$

$f'(x) = \frac{( {x}^{6} - 1)' \times \sin(x) - (\sin(x))' ( {x}^{6} - 1) }{ \sin {}^{2} (x) } = \\ = \frac{6 {x}^{5} \sin(x) - \cos(x) \times ( {x}^{6} - 1) }{ \sin {}^{2} (x) }$

5

$f'(x) = ( {x}^{4} - 3)'(x + 4) + (x + 4)'( {x}^{4} - 3) = \\ = 4 {x}^{3} (x + 4) + 1 \times ( {x}^{4} - 3) = \\ = 4 {x}^{4} + 16 {x}^{3} + {x}^{4} - 3 = \\ = 5 {x}^{4} + 16 {x}^{3} - 3$

6

$f'(x) = 7 (5 {x}^{6} - 4) {}^{6} \times (5 {x}^{6} - 4) '= \\ = 7 {(5 {x}^{6} - 4) }^{6} \times 30 {x}^{5} = \\ = 210 {x}^{ 5} {(5 {x}^{6} - 4) }^{6}$

7

$f'(x) =( {(3 - {x}^{5}) }^{ \frac{1}{2} } ) '= \frac{1}{2} {(3 - {x}^{5} )}^{ - \frac{1}{2} } \times (3 - {x}^{5} ) '= \\ = \frac{1}{2 \sqrt{3 - {x}^{5} } } \times ( - 5 {x}^{4} ) = - \frac{5 {x}^{4} }{2 \sqrt{3 - {x}^{5} } }$

Answer 2

Ответ:

′

(x)=5×6x

5

−8+0=30x

5

−8

2

\begin{gathered}f(x) = \frac{3 }{ {x}^{8} } - \frac{ {x}^{9} }{3} + 6 \sqrt{x} = \\ = 3 {x}^{ - 8} - \frac{ {x}^{9} }{3} + 6 {x}^{ \frac{1}{2} } \end{gathered}

f(x)=

x

8

3

−

3

x

9

+6

x

=

=3x

−8

−

3

x

9

+6x

2

1

\begin{gathered}f'(x) = 3 \times ( - 8) {x}^{ - 9} - \frac{1}{3} \times 9 {x}^{8} + 6 \times \frac{1}{2} {x}^{ - \frac{1}{2} } = \\ = - \frac{24}{ {x}^{9} } - 3 {x}^{8} + \frac{3}{ \sqrt{x} } \end{gathered}

f

′

(x)=3×(−8)x

−9

−

3

1

×9x

8

+6×

2

1

x

−

2

1

=

=−

x

9

24

−3x

8

+

x

3

3

\begin{gathered}f'(x) = (tgx)'(x - 4) + ( x - 4)' \times tgx = \\ = \frac{x - 4}{ \cos {}^{2} (x) } + tgx\end{gathered}

f

′

(x)=(tgx)

′

(x−4)+(x−4)

′

×tgx=

=

cos

2

(x)

x−4

+tgx

4

\begin{gathered}f(x) = \frac{ {x}^{6} - 1} { \sin(x) } \\ \end{gathered}

f(x)=

sin(x)

x

6

−1

\begin{gathered}f'(x) = \frac{( {x}^{6} - 1)' \times \sin(x) - (\sin(x))' ( {x}^{6} - 1) }{ \sin {}^{2} (x) } = \\ = \frac{6 {x}^{5} \sin(x) - \cos(x) \times ( {x}^{6} - 1) }{ \sin {}^{2} (x) } \end{gathered}

f

′

(x)=

sin

2

(x)

(x

6

−1)

′

×sin(x)−(sin(x))

′

(x

6

−1)

=

=

sin

2

(x)

6x

5

sin(x)−cos(x)×(x

6

−1)

5

\begin{gathered}f'(x) = ( {x}^{4} - 3)'(x + 4) + (x + 4)'( {x}^{4} - 3) = \\ = 4 {x}^{3} (x + 4) + 1 \times ( {x}^{4} - 3) = \\ = 4 {x}^{4} + 16 {x}^{3} + {x}^{4} - 3 = \\ = 5 {x}^{4} + 16 {x}^{3} - 3\end{gathered}

f

′

(x)=(x

4

−3)

′

(x+4)+(x+4)

′

(x

4

−3)=

=4x

3

(x+4)+1×(x

4

−3)=

=4x

4

+16x

3

+x

4

−3=

=5x

4

+16x

3

−3

6

\begin{gathered}f'(x) = 7 (5 {x}^{6} - 4) {}^{6} \times (5 {x}^{6} - 4) '= \\ = 7 {(5 {x}^{6} - 4) }^{6} \times 30 {x}^{5} = \\ = 210 {x}^{ 5} {(5 {x}^{6} - 4) }^{6} \end{gathered}

f

′

(x)=7(5x

6

−4)

6

×(5x

6

−4)

′

=

=7(5x

6

−4)

6

×30x

5

=

=210x

5

(5x

6

−4)

6

7

\begin{gathered}f'(x) =( {(3 - {x}^{5}) }^{ \frac{1}{2} } ) '= \frac{1}{2} {(3 - {x}^{5} )}^{ - \frac{1}{2} } \times (3 - {x}^{5} ) '= \\ = \frac{1}{2 \sqrt{3 - {x}^{5} } } \times ( - 5 {x}^{4} ) = - \frac{5 {x}^{4} }{2 \sqrt{3 - {x}^{5} } } \end{gathered}

f

′

(x)=((3−x

5

)

2

1

)

′

=

2

1

(3−x

5

)

−

2

1

×(3−x

5

)

′

=

=

2

3−x

5

1

×(−5x

4

)=−

2

3−x

5

5x

4