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Find the first partial derivatives of the function. z = x sin(xy)?
Differentiating with respect to a single variable while keeping other variables as constants in the expression is known as Partial differentiation.
Answer: The first partial derivatives of the function. z = x sin(xy) are sin(xy) + xy cos(xy) and x2cos(xy).
Let's go through the explanation to understand better.
Explanation:
Let z = x sin(xy)
Differentiate the function z = x sin(xy) w.r.t. x, and treat y as a constant.
d[z]/dx = d[ x sin(xy)]/dx
d[z]/dx = 1⋅sin(xy) + cos(xy)(y)⋅x
d[z]/dx = sin(xy) + xy cos(xy)
Now, Differentiate the function z = x sin(xy) w.r.t. y, and treat x as a constant.
d[z]/dy = d[ x sin(xy)]/dy
⇒ d[z]/dy = x⋅cos(xy)(x)
⇒ d[z]/dy = x2cos(xy)
A Cuemath's Partial Derivative Calculator helps to calculate the value of the partial derivatives.
Thus, the first partial derivatives of the function. z = x sin(xy) are sin(xy) + xy cos(xy) and x2cos(xy).
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