Prove the following property about subdifferential, affline transformation. - əf(x) = {Vf(x)} if ƒ is differentiable at r – affine transformation of variables: if g(x) = f(Ax +b), then dg(x) = ATaf(Ax + b)

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A: factors of 24 that add up to 10

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A: given letters: A,T,C and Gtotal number of letters = 4

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A: We will solve the problem.

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A: Explanation and solutions is given below.....

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A: given , number of partitions of n into k parts  we have to prove that , partitions of number n + k…

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A: Consider the given expression

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A: Given: 30 total M&Ms in that 10 red M&Ms.

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A: Solution: The objective is to find the value of the given expression

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A: Given that 5712+134+412Solution  :5712+134+412=57+39+24612

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A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

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A: Case 1: Let the given number be in mixed fraction notation.

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Q: | (16 – 2*) dz =

A: To find : the value of ∫0216-x4dx   Using the formula ∫abxndx=1n+1bn+1-an+1

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A: Here we find Laplace inverse transform

Q: 5. Find the coefficient of a¹¹b4 in the expansion of (a + b)¹5.

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Q: 6（c)(d)

A: We shall use the properties of homomorphism to solve this question