Question : 131) f(x ,y, z) = (sin xy)(cos yz2) A) ∂f/∂x = : 1757194

131) f(x ,y, z) = (sin xy)(cos yz²)

A) ∂f/∂x = (y cos xy)(cos yz²); ∂f/∂y = (z² sin xy)(sin yz²)- (x cos xy)(cos yz²); ∂f

∂z = 2(yz sin xy)(sinyz²)

B) ∂f/∂x = (y cos xy)(cos yz²); ∂f/∂y = (x cos xy)(cos yz²) - (z² sin xy)(sin yz²); ∂f/∂z = 2(yz sin xy)(sinyz²)

C) ∂f/∂x = (y cos xy)(cosyz²); ∂f/∂y = (x cos xy)(cos yz²) - (z² sin xy)(sin yz²); ∂f/∂z = -2(yz sin

xy)(sin yz²)

D) ∂f/∂x = (y cos xy)(cos yz²); ∂f/∂y = (x cos xy)(cos yz²); ∂f/∂z = -2(yz sin xy)(sin yz²)

132) f(x, y, z) = z(ex)y

A) ∂f/∂x = zyexy; ∂f/∂y = zxexy; ∂f/∂z = zexy B) ∂f/∂x = zexy; ∂f/∂y = zexy; ∂f/∂z = exy

C) ∂f/∂x = zyexy; ∂f/∂y = zxexy; ∂f/∂z = exy D) ∂f/∂x = zxexy; ∂f/∂y = zyexy; ∂f/∂z = exy

133) f(x,y,z) = xe(x² + y² + z²)

A) ∂f/∂x = (1 + 2x²) e(x² + y² + z²); ∂f/∂y = xy²e(x² + y² + z²); ∂f/∂z = xz²e(x² + y² + z²)

B) ∂f/∂x = 2x²e(x² + y² + z²); ∂f/∂y = xye(x² + y² + z²); ∂f/∂z = 2xze(x² + y² + z²)

C) ∂f/∂x = (1 + 2x²) e(x² + y² + z²); ∂f/∂y = xe(x² + y² + z²); ∂f/∂z = xe(x² + y² + z²)

D) ∂f/∂x = (1 + 2x²) e(x² + y² + z²); ∂f/∂y = 2xye(x² + y² + z²); ∂f/∂z = 2xze(x² + y² + z²)

134) f(x, y, z) =

135) f(x, y, z) = cos x sin2 yz

A) ∂f/∂x = sin x sin2 yz; ∂f/∂y = -2z cos x sin yz cos yz; ∂f/∂z = - 2y cos x sin yz cos yz

B) ∂f/∂x = sin x sin2 yz; ∂f/∂y = - cos x sin yz cos yz; ∂f/∂z = -cos x sin yz cos yz

C) ∂f/∂x = -sin x sin2 yz; ∂f/∂y = z cos x sin yz cos yz; ∂f/∂z = y cos x sin yz cos yz

D) ∂f/∂x = -sin x sin2 yz; ∂f/∂y = 2z cos x sin yz cos yz ; ∂f/∂z = 2y cos x sin yz cos yz

136) f(x, y, z) = cos y/xz²

137) f(x, y, z) = e(sin (x) + yz)

A) ∂f/∂x = cos(x)e(sin (x) + yz); ∂f/∂y = e(sin (x) + yz); ∂f/∂z = e(sin (x) + yz)

B) ∂f/∂x = cos(x) + yz e(sin (x) + yz); ∂f/∂y = ze(sin (x) + yz); ∂f/∂z = ye(sin (x) + yz)

C) ∂f/∂x = cos(x) e(sin (x) + yz); ∂f/∂y = ze(sin (x) + yz); ∂f/∂z = ye(sin (x) + yz)

D) ∂f/∂x = e(sin (x) + yz); ∂f/∂y = ze(sin (x) + yz); ∂f/∂z = ye(sin (x) + yz)

138) The Van derWaals equation provides an approximate model for the behavior of real gases. The equation is P(V, T) = RT/V - b - a/V2 , where P is pressure, V is volume, T is Kelvin temperature, and a,b , and R are constants. Find the partial derivative of the function with respect to each variable.

139) The Redlich-Kwong equation provides an approximate model for the behavior of real gases. The equation is P(V, T) = RT/V - b - a/T1/2V(V + b) , where P is pressure, V is volume, T is Kelvin temperature, and a,b , and R are constants. Find the partial derivative of the function with respect to each variable.

140) w(x, t) = sin (2x + 2ct)

A) No B) Yes