About the Project

derivatives

AdvancedHelp

(0.001 seconds)

1—10 of 272 matching pages

1: 4.20 Derivatives and Differential Equations
§4.20 Derivatives and Differential Equations
4.20.1 d d z sin z = cos z ,
4.20.2 d d z cos z = sin z ,
4.20.3 d d z tan z = sec 2 z ,
4.20.4 d d z csc z = csc z cot z ,
2: 4.34 Derivatives and Differential Equations
§4.34 Derivatives and Differential Equations
4.34.1 d d z sinh z = cosh z ,
4.34.2 d d z cosh z = sinh z ,
4.34.7 d 2 w d z 2 a 2 w = 0 ,
4.34.8 ( d w d z ) 2 a 2 w 2 = 1 ,
3: 4.7 Derivatives and Differential Equations
§4.7 Derivatives and Differential Equations
§4.7(i) Logarithms
4.7.1 d d z ln z = 1 z ,
§4.7(ii) Exponentials and Powers
4.7.12 d w d z = f ( z ) w
4: 22.13 Derivatives and Differential Equations
§22.13 Derivatives and Differential Equations
§22.13(i) Derivatives
Table 22.13.1: Derivatives of Jacobian elliptic functions with respect to variable.
d d z ( sn z ) = cn z dn z d d z ( dc z )  = k 2 sc z nc z
Note that each derivative in Table 22.13.1 is a constant multiple of the product of the corresponding copolar functions. …
22.13.1 ( d d z sn ( z , k ) ) 2 = ( 1 sn 2 ( z , k ) ) ( 1 k 2 sn 2 ( z , k ) ) ,
5: 7.10 Derivatives
§7.10 Derivatives
7.10.1 d n + 1 erf z d z n + 1 = ( 1 ) n 2 π H n ( z ) e z 2 , n = 0 , 1 , 2 , .
d f ( z ) d z = π z g ( z ) ,
d g ( z ) d z = π z f ( z ) 1 .
6: 36.10 Differential Equations
§36.10(ii) Partial Derivatives with Respect to the x n
36.10.10 3 n Ψ 3 y 3 n = i n 2 n Ψ 3 z 2 n .
§36.10(iv) Partial z -Derivatives
7: 1.5 Calculus of Two or More Variables
§1.5(i) Partial Derivatives
The function f ( x , y ) is continuously differentiable if f , f / x , and f / y are continuous, and twice-continuously differentiable if also 2 f / x 2 , 2 f / y 2 , 2 f / x y , and 2 f / y x are continuous. …
Chain Rule
Suppose that a , b , c are finite, d is finite or + , and f ( x , y ) , f / x are continuous on the partly-closed rectangle or infinite strip [ a , b ] × [ c , d ) . …
§1.5(vi) Jacobians and Change of Variables
8: 14.29 Generalizations
14.29.1 ( 1 z 2 ) d 2 w d z 2 2 z d w d z + ( ν ( ν + 1 ) μ 1 2 2 ( 1 z ) μ 2 2 2 ( 1 + z ) ) w = 0
9: 19.18 Derivatives and Differential Equations
§19.18 Derivatives and Differential Equations
§19.18(i) Derivatives
Let j = / z j , and 𝐞 j be an n -tuple with 1 in the j th place and 0’s elsewhere. …
19.18.14 2 w x 2 = 2 w y 2 + 1 y w y .
19.18.15 2 W t 2 = 2 W x 2 + 2 W y 2 .
10: 30.12 Generalized and Coulomb Spheroidal Functions
30.12.1 d d z ( ( 1 z 2 ) d w d z ) + ( λ + α z + γ 2 ( 1 z 2 ) μ 2 1 z 2 ) w = 0 ,
30.12.2 d d z ( ( 1 z 2 ) d w d z ) + ( λ + γ 2 ( 1 z 2 ) α ( α + 1 ) z 2 μ 2 1 z 2 ) w = 0 ,