Determine the derivatives, dy da dy da (1) y=e¹ ⇒ (2) y=x4 ⇒ dy da Y of the four given curves.

Q: The equation of the tangent line to the curve z +y = 25, at (4,-16) is 4 y%= %3D 16 16 (z - 4) + 16…

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Q: Find the coordinates of the point where the equation y' – xy = 2 has a vertical tangent.

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Q: whose equation is y³ + 2xy + x² = 9 Using techniques we have learned in our course, perform the…

A: Given query is to find the derivative and equation of the tangent.

Q: d two coordinate points at which the tangent line to the curve given by x² – 2x + 4y² = 15 is…

A: if the tangent is vertical then dydx will be ∞x2-2x+4y2=15differentiate 2x-2+8ydydx=04ydydx=1-xsince…

Q: Find the equation of the tangent line to the curve x=t2−2t, y=t2+2t at the point t=2.

A: Given equation of curve is Now,

Q: Show that the equation of the tangent to the curve = 2 (a'0, b1.0) a y at the point (a, b) is = 2.…

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Q: 2. Find the equation of the tangent line to y = x² + 2 at x = -2.

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Q: Find an equation of the tangent line to the curve y = 4 z³+x+9 at x = -2. Enter your equation in the…

A: The equation of the tangent line is given by:Where