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antiseptic1488 [7]
3 years ago
15

Differentiate. y = log₅(2x³-1)

Mathematics
2 answers:
likoan [24]3 years ago
8 0
(1/(ln 5))((6x^2)/(2x^3-1))

Sonja [21]3 years ago
8 0
Change the base to ln

remmber
log_a(b)= \frac{log_c(b)}{log_c(a)}
ln is just base e

so
log_5(2x^3-1)= \frac{log_e(2x^3-1)}{log_e(5)} = \frac{ln(2x^3-1))}{ln(5)}

remember that tthe deritivive of \frac{f(x)}{g(x)} is \frac{f'(x)g(x)-g'(x)f(x)}{g(x)^2}
so

let's take the deritivies seperately first
deritivive of ln(2x^3-1) is \frac{6x^2}{2x^3-1}
deritivive of ln(5) is 0


\frac{ln(2x^3-1))}{ln(5)} = \frac{( \frac{6x^2}{2x^3-1})(ln(5))-(0)(ln(2x^3-1))}{(ln(5))^2}=\frac{( \frac{6x^2}{2x^3-1})(ln(5))}{(ln(5))^2}=\frac{ \frac{6x^2}{2x^3-1}}{ln(5)}= \frac{6x^2}{(2x^3-1)(ln(5))}


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