find all second order derivatives for ( z = 7ye^{6x} ).\n( z_{xx}=252ye^{6x} )\n( z_{yy}=)
find all second order derivatives for ( z = 7ye^{6x} ).\n( z_{xx}=252ye^{6x} )\n( z_{yy}=)
Answer
Explanation:
Step1: Find the first - order derivative with respect to (y)
Given (z = 7ye^{6x}). Using the rule (\frac{\partial}{\partial y}(ay)=a) (where (a = 7e^{6x})), we have (z_y=\frac{\partial z}{\partial y}=7e^{6x}).
Step2: Find the second - order derivative with respect to (y)
Differentiate (z_y = 7e^{6x}) with respect to (y). Since (\frac{\partial}{\partial y}(c)=0) (where (c = 7e^{6x}) is a constant with respect to (y)), we get (z_{yy}=\frac{\partial^2 z}{\partial y^2}=0).
Answer:
(z_{yy}=0)