Find dy.
-
A) 14x + 6 dx
B) 14x dx
C) 14x + 3 dx
D) (14x + 3) dx

Question

Find dy.
-
A) 14x + 6 dx 
B) 14x dx 
C) 14x + 3 dx 
D) (14x + 3) dx

Quizplus · Accepted Answer

The given expression has "dy" but no explicit function of "x", so we need to find the implicit derivative. Taking derivative of both sides with respect to "x", we get:
dy/dx = (3x^2 + 7)/(2y)

Now multiply both sides by "dx":
dy = (3x^2 + 7)/(2y) dx

This matches the form (14x + 3) dx, so the answer is D. Given equation: 11ebb6d7_48ce_8547_b437_37feeeda8893_TB8593_11
We need to find dy, which means we need to differentiate the equation with respect to y, assuming x as a constant. 
∴ dy/dx (14x^2y^3 + 3xy^2 - 7y) = (d/dy)(14x^2y^3) + (d/dy)(3xy^2) - (d/dy)(7y)
= (14x^2*3y^2) + (3x*2y) - 7
= 42x^2y^2 + 6xy - 7
Hence, dy = (42x^2y^2 + 6xy - 7)dx
= 14x(3y^2)dx + 3(2xy)dx - 7dx
= (14x+3)dx

Find Dy. -A) 14x + 6 Dx