#12: use the definition of the derivative to calculate the derivative of f(x)=9x^2

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A: we can solve as follows

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A: To solve: y(x2 - y2 + 1)dx - x(x2 - y2 - 1)dy = 0 ⇒yx2 dx- y3 dx+ y dx - x3dy +xy2dy +xdy = 0

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A: Area of a rectangle= length × breadth

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: for orthogonal of vector dot product of vector is 0 a*b=0 (ci+j)(8i+24j) = 0 8c +24 = 0 8c =-24 c…

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A: If you submitted multiple posts for this same problem, that will go to different experts. So you…

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A: Given  z = x2 sinh-1x-y4 We have to find  ∂2z∂x∂y.

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A: a) From the table we get take points: -3, 4.333, -2, 5, -1, 6. We plug them in the exponential…

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A: Suppose ∫0afx dx=A. To explain graphically what the value of the integral below is when fx is an odd…

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A: Here, the given series is: ∑n=2∞(n-3)Anxn-5...(1)

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Q: dt if t = (6r³ +3r² )* and w=| dw =(r² + 2r – 5)* Determine 9r* (2r +1)(3r +1) (r+1)(r² +2r – 5) b.…

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A: find the components

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A: We will find the unit vector satisfying the given conditions in the following step.

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A: Given that      2(sin(t))2 - sin(t) -1 = 0

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: Given problem:- Use Lagrange multipliers to find the maximum and minimum values off subject to the…

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Q: d Calculate ri(t) · r2(t)] and ri(t) × r2(t)] first by differentiating d dt dt the product directly…

A: We know, d/dt (r1(t).r2(t))= r1(t).dr2(t)/dt + r2(t).dr1(t)/dt