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Answer:
a) 6x²/2x³-4
b)
Step-by-step explanation:
a) Given the ln(2x³-4). We will use the chain rule in differentiating the function
If y = ln(2x³-4);
u = 2x³-4; du/dx = 3(2)x³⁻¹
du/dx = 6x²
y = ln u; dy/du = 1/u
According to chain rule, dy/dx = dy/dy*du/dx
dy/dx = 1/u * 6x²
dy/dx = 1/2x³-4 * 6x²
dy/dx = 6x²/2x³-4
Hence, the derivative of the given function is 6x²/2x³-4
b) Given an integral function , the integral problem can be solved using integration by substitution method as shown below;
From the question, let y = 2x³-4... 1, dy/dx = 6x²
dx = dy/6x² ... 2
Substituting equation 1 and 2 into the question given;