Derivative of y=log base 2(2x+1)^3

There are two interpretations.

①:

log 2 [(2x + 1)^3]

②:

[log 2 (2x + 1)]^3

①:

d/dx log 2 [(2x + 1)^3]

= 1/{[(2x + 1)^3] ln (2)}

= [3(2x + 1)^2]/{[(2x + 1)^3] ln (2)}

= [2 * 3(2x + 1)^2]/{[(2x + 1)^3] ln (2)}

= [6(2x + 1)^2]/{[(2x + 1)^3] ln (2)}

②:

d/dx [log 2 (2x + 1)]^3

= 3[log 2 (2x + 1)]^2

= {3[log 2 (2x + 1)]^2}/[(2x + 1) ln (2)]

= {2 * 3[log 2 (2x + 1)]^2}/[(2x + 1) ln (2)]

= {6[log 2 (2x + 1)]^2}/[(2x + 1) ln (2)]

Step-by-step explanation:

Chain rule:

d/dx f(g(h... w(x)))

= f’(g(h(... w(x * g’(h(... w(x))) * h’(... w(x)) * ... * w’(x)

You derive functions inside another function by differentiating the outer function while leaving the insides intact, then multiplying with the derivative of the function inside it while leaving the insides intact, and so on and so on until the innermost one.

Derivatives of the functions:

d/dx x^n = nx^(n - 1)

d/dx log n (x) = 1/[x ln (n)]

image result for what is another name for consecutive interior angles? ​

when two lines are crossed by another line (called the transversal): the pairs of angles on one side of the transversal but inside the two lines are called consecutive interior angles. in this example, these are consecutive interior angles: d and f.

step-by-step explanation:

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step-by-step explanation: