Question Detail
Question
The
d/dx(7^(5x-1) + log_7|5x²-x|) equals
Correct Answer
Option A is the correct answer.
Detailed Explanation
We need to find the derivative of
y = 7^(5x-1) + log_7|5x²-x|.- For the first term,
d/dx(a^u) = a^u * ln(a) * du/dx:d/dx(7^(5x-1)) = 7^(5x-1) * ln(7) * d/dx(5x-1)= 7^(5x-1) * ln(7) * 5= 5 * 7^(5x-1)ln(7) - For the second term,
d/dx(log_a|u|) = (1/(u ln(a))) * du/dx:d/dx(log_7|5x²-x|) = (1/((5x²-x)ln(7))) * d/dx(5x²-x)= (1/((5x²-x)ln(7))) * (10x-1)= (10x-1) / ((5x²-x)ln(7)) - Combine the derivatives of both terms:
dy/dx = 5 * 7^(5x-1)ln(7) + (10x-1) / ((5x²-x)ln(7))
Hint
Recall the derivative rules for exponential functions
a^u and logarithmic functions log_a|u|. Remember to apply the chain rule correctly for both terms.