What is the derivative of (log_{10}(x^3+4))^5 ?

The derivative of (log_{10}(x^3+4))^5 is (15x^2log_{10}(x^3+4)^4)/(ln(10)(x^3+4))

What is the first derivative of (log_{10}(x^3+4))^5 ?

The first derivative of (log_{10}(x^3+4))^5 is (15x^2log_{10}(x^3+4)^4)/(ln(10)(x^3+4))

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derivative of

(lo g_{10} (x^{3} + 4))^{5}

\frac{15 x ^{2} lo g _{10} ( x ^{3} + 4 ) ^{4}}{ln ( 10 ) ( x ^{3} + 4 )}

Solution steps

\frac{d}{d x} ((lo g_{10} (x^{3} + 4))^{5})

Apply the chain rule:

5 (lo g_{10} (x^{3} + 4))^{4} \frac{d}{d x} (lo g_{10} (x^{3} + 4))

= 5 (lo g_{10} (x^{3} + 4))^{4} \frac{d}{d x} (lo g_{10} (x^{3} + 4))

\frac{d}{d x} (lo g_{10} (x^{3} + 4)) = \frac{3 x ^{2}}{ln ( 10 ) ( x ^{3} + 4 )}

= 5 (lo g_{10} (x^{3} + 4))^{4} \frac{3 x ^{2}}{ln ( 10 ) ( x ^{3} + 4 )}

Simplify

5 lo g_{10} (x^{3} + 4)^{4} \frac{3 x ^{2}}{ln ( 10 ) ( x ^{3} + 4 )} : \frac{15 x ^{2} lo g _{10} ( x ^{3} + 4 ) ^{4}}{ln ( 10 ) ( x ^{3} + 4 )}

= \frac{15 x ^{2} lo g _{10} ( x ^{3} + 4 ) ^{4}}{ln ( 10 ) ( x ^{3} + 4 )}

What is the derivative of (log_{10}(x^3+4))^5 ?
The derivative of (log_{10}(x^3+4))^5 is (15x^2log_{10}(x^3+4)^4)/(ln(10)(x^3+4))
What is the first derivative of (log_{10}(x^3+4))^5 ?
The first derivative of (log_{10}(x^3+4))^5 is (15x^2log_{10}(x^3+4)^4)/(ln(10)(x^3+4))