Question

Чему равны частные производные первого порядка функции : z=ctg(x^4*y^4), z=tg(x^4*y^7), z=tg(x^5*y^4) ,z=cos(x^3*y^3)

Answer 1

1.

$z = ctg( {x}^{4} {y}^{4} )$

$Z'x = - \frac{1}{ { \sin}^{2}( {x}^{4} {y}^{4}) } \times 4 {x}^{3} {y}^{4} \\$

$Z'y = - \frac{1}{ { \sin}^{2} ( {x}^{4} {y}^{4} )} \times 4 {y}^{3} {x}^{4} \\$

2.

$z = tg( {x}^{4} {y}^{7} )$

$Z'x = \frac{1}{ { \cos }^{2} ( {x}^{4} {y}^{7}) } \times 4 {x}^{3} {y}^{7} \\$

$Z'y = \frac{1}{ { \cos }^{2} ( {x}^{4} {y}^{7}) } \times 7 {y}^{6} {x}^{4} \\$

3.

$z = tg( {x}^{5} {y}^{4} )$

$Z'x = \frac{1}{ { \cos}^{2}( {x}^{5} {y}^{4}) } \times 5 {x}^{4} {y}^{4} \\$

$Z'y = \frac{1}{ { \cos }^{2}( {x}^{5} {y}^{4} ) } \times 4 {y}^{3} {x}^{5} \\$

4.

$z = \cos( {x}^{3} {y}^{3} )$

$Z'x = - \sin( {x}^{3} {y}^{3} ) \times 3 {x}^{2} {y}^{3}$

$Z'y = - \sin( {x}^{3} {y}^{3} ) \times 3 {y}^{2} {x}^{}$