Math Problem Statement

Find the derivative of f left parenthesis x right parenthesis equals 2 x to the power of 4 5 to the power of 9 x plus 1 end exponent.

f apostrophe left parenthesis x right parenthesis equals 8 x cubed times 5 to the power of 9 x plus 1 end exponent plus 18 x to the power of 4 times 5 to the power of 9 x plus 1 end exponent

f apostrophe left parenthesis x right parenthesis equals 8 x cubed times 5 to the power of 9 x plus 1 end exponent ln 5

f apostrophe left parenthesis x right parenthesis equals 8 x cubed times 5 to the power of 9 x plus 1 end exponent plus 18 x to the power of 4 times 5 to the power of 9 x plus 1 end exponent ln 5

f apostrophe left parenthesis x right parenthesis equals 72 x cubed times 5 to the power of 9 x plus 1 end exponent ln 5

Solution

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Math Problem Analysis

Mathematical Concepts

Differentiation
Product Rule
Chain Rule
Exponential Functions

Formulas

Product rule: (fg)' = f'g + fg'
Chain rule: d/dx [a^(bx + c)] = a^(bx + c) * ln(a) * b

Theorems

Product Rule
Chain Rule

Suitable Grade Level

Undergraduate Calculus