What is the derivative of ln((x^2+4x+5^3)) ?

The derivative of ln((x^2+4x+5^3)) is (3(2x+4))/(x^2+4x+5)

What is the first derivative of ln((x^2+4x+5^3)) ?

The first derivative of ln((x^2+4x+5^3)) is (3(2x+4))/(x^2+4x+5)

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Popular >

\frac{d}{d x} (ln ((x^{2} + 4 x + 5)^{3}))

\frac{3 ( 2 x + 4 )}{x ^{2} + 4 x + 5}

Solution steps

\frac{d}{d x} (ln ((x^{2} + 4 x + 5)^{3}))

Apply the chain rule:

\frac{1}{( x ^{2} + 4 x + 5 ) ^{3}} \frac{d}{d x} ((x^{2} + 4 x + 5)^{3})

= \frac{1}{( x ^{2} + 4 x + 5 ) ^{3}} \frac{d}{d x} ((x^{2} + 4 x + 5)^{3})

\frac{d}{d x} ((x^{2} + 4 x + 5)^{3}) = 3 (x^{2} + 4 x + 5)^{2} (2 x + 4)

= \frac{1}{( x ^{2} + 4 x + 5 ) ^{3}} \cdot 3 (x^{2} + 4 x + 5)^{2} (2 x + 4)

Simplify

\frac{1}{( x ^{2} + 4 x + 5 ) ^{3}} \cdot 3 (x^{2} + 4 x + 5)^{2} (2 x + 4) : \frac{3 ( 2 x + 4 )}{x ^{2} + 4 x + 5}

= \frac{3 ( 2 x + 4 )}{x ^{2} + 4 x + 5}

\int e - e^{x} d x

\frac{1}{2} sin (4 t)

x y^{^{'}} + y = - 3 x

\int \frac{1}{( v + 7 ) ^{3}} d v

f (x) = x^{2 π}

What is the derivative of ln((x^2+4x+5^3)) ?
The derivative of ln((x^2+4x+5^3)) is (3(2x+4))/(x^2+4x+5)
What is the first derivative of ln((x^2+4x+5^3)) ?
The first derivative of ln((x^2+4x+5^3)) is (3(2x+4))/(x^2+4x+5)