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Popular >

derivative of ln((5x^2))

Solution

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

Solution

\frac{2}{x}

Solution steps

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

Simplify

ln ((5 x)^{2}) : ln (25 x^{2})

= \frac{d}{d x} (ln (25 x^{2}))

Apply the chain rule:

\frac{1}{25 x ^{2}} \frac{d}{d x} (25 x^{2})

= \frac{1}{25 x ^{2}} \frac{d}{d x} (25 x^{2})

\frac{d}{d x} (25 x^{2}) = 50 x

= \frac{1}{25 x ^{2}} \cdot 50 x

Simplify

\frac{1}{25 x ^{2}} \cdot 50 x : \frac{2}{x}

= \frac{2}{x}

Popular Examples

y^{^{''}} + 7 y^{^{'}} = 0

derivative of cot(3-2x)

\frac{d}{d x} (cot (3 - 2 x))

(d^2y)/(dt^2)+5(dy)/(dt)+6y=1

\frac{d ^{2} y}{d t ^{2}} + 5 \frac{d y}{d t} + 6 y = 1

xy^2y^'=y^3-4x^3,y(1)=4

x y^{2} y^{^{'}} = y^{3} - 4 x^{3}, y (1) = 4

inverse oflaplace ((-1/4))/(1+(1/2)*s)inverse laplace

\frac{( - \frac{1}{4} )}{1 + ( \frac{1}{2} ) \cdot s}

Frequently Asked Questions (FAQ)

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