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Popular >

derivative of ln((x^2+4^5))

Solution

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

Solution

\frac{10 x}{x ^{2} + 4}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} ((x^{2} + 4)^{5}) = 10 x (x^{2} + 4)^{4}

= \frac{1}{( x ^{2} + 4 ) ^{5}} \cdot 10 x (x^{2} + 4)^{4}

Simplify

\frac{1}{( x ^{2} + 4 ) ^{5}} \cdot 10 x (x^{2} + 4)^{4} : \frac{10 x}{x ^{2} + 4}

= \frac{10 x}{x ^{2} + 4}

Popular Examples

limit as x approaches 4 of ((2))/(x-4)

x \to 4 lim (\frac{( 2 )}{x - 4})

limit as x approaches 2-of (2x)/(x^2-4)

x \to 2 - lim (\frac{2 x}{x ^{2} - 4})

y^{''}+8y^'+25y=0,y(0)=3,y^'(0)=-10

y^{^{''}} + 8 y^{^{'}} + 25 y = 0, y (0) = 3, y^{^{'}} (0) = - 10

limit as x approaches-2+of (-7x)/(x+2)

x \to - 2 + lim (\frac{- 7 x}{x + 2})

integral of 7*tan^3(x)sec(x)

\int 7 \cdot tan^{3} (x) sec (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of ln((x^2+4^5)) ?
The derivative of ln((x^2+4^5)) is (10x)/(x^2+4)
What is the first derivative of ln((x^2+4^5)) ?
The first derivative of ln((x^2+4^5)) is (10x)/(x^2+4)