The table shows some values of the derivative of an unknown function f.Complete the table by finding the derivative of each transformation of f, it possible a) g(x)=f(x) − 2 b) h(x)=2f(x) c) r(x)=f(−3x)

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The table shows some values of the derivative of an unknown function f.Complete the table by finding the derivative of each transformation of f, it possible  a) g(x)=f(x) − 2  b) h(x)=2f(x)  c) r(x)=f(−3x)

ottcomn · Accepted Answer

Step 1The derivative properties:ddx(f(x) − a)=f′(x)ddx(af(x))=af′(x)calculate the derivative of g(x)=f(x) − 2 with respect to x as followsg′(x)=ddx(f(x) − 2)=f′(x)Step 2Now calculate the derivative of h(x)=2f(x) with respect to x as followsh′(x)=ddx=(2f(x))=2f′(x)∴h′(x)=2f′(x)Step 3Now calculate the derivative of r(x)=f(−3x) with respect to x as followsr′(x)=ddx=f(−3x)= −3f′(−3x)As r′(x)= −3f′(−3x), compute the the value of −3f′(−3x)r′(−2)=3f′[−3 (2)]=−3f′(6)Here r′(−2)= −3f′(6) cannot be computed the valuesof f′(6) is not known.r′(−1)= −3f′[−3 (−1)]= −3f′(3)= −3(−5)=15r′(0)= −3f′[−3 (0)]=−3(−13)=1And r′(1)= −3f[−3 (1)]= −3f′(−3)Hense −3f′(−3) can not be compluted.

alenahelenash · Accepted Answer

Here are the derivatives of each transformation of the unknown function f:a) g(x)=f(x)−2To find the derivative of g(x), we need to differentiate f(x) with respect to x. Since -2 is a constant, its derivative is 0. Thus, the derivative of g(x) is the same as the derivative of f(x):dgdx=dfdxb) h(x)=2f(x)To find the derivative of h(x), we differentiate 2f(x) with respect to x. Using the constant multiple rule, we know that the derivative of a constant (in this case, 2) times a function (f(x)) is equal to the constant times the derivative of the function:dhdx=2·dfdxc) r(x)=f(−3x)To find the derivative of r(x), we differentiate f(-3x) with respect to x. Using the chain rule, we multiply the derivative of the outer function (f) with the derivative of the inner function (-3x):drdx=dfd(−3x)·d(−3x)dxTo simplify further, we know that d(−3x)dx=−3:drdx=dfd(−3x)·(−3)

xleb123 · Accepted Answer

a) Let&#039;s find the derivative of the function g(x) = f(x) - 2. To differentiate g(x), we need to differentiate each term separately. Since the derivative of a constant (in this case, -2) is zero, we only need to find the derivative of f(x). Let&#039;s denote the derivative of f(x) as f&#039;(x). Therefore, the derivative of g(x) is given by:g′(x)=f′(x)−0=f′(x)b) Now, let&#039;s find the derivative of the function h(x) = 2f(x). Similar to part a, the derivative of a constant (in this case, 2) is zero, so we only need to find the derivative of f(x). Using the product rule, the derivative of h(x) is given by:h′(x)=2·f′(x)c) Lastly, let&#039;s find the derivative of the function r(x) = f(-3x). To find the derivative of r(x), we need to apply the chain rule. Let&#039;s denote the derivative of f(-3x) as f&#039;(-3x). Using the chain rule, the derivative of r(x) is given by:r′(x)=f′(−3x)·(−3)These are the derivatives of the given transformations of the unknown function f.

The table shows some values of the derivative of an unknown function f.Complete the table by finding the derivative of each transformation of f, it possible a) g(x) = f(x) - 2 b) h(x) = 2 f(x) c) r(x) = f(-3x)

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