What is the derivative of (log_{5}(x))/(6+x^5) ?

The derivative of (log_{5}(x))/(6+x^5) is (6+x^5-5x^5ln(x))/(ln(5)x(6+x^5)^2)

What is the first derivative of (log_{5}(x))/(6+x^5) ?

The first derivative of (log_{5}(x))/(6+x^5) is (6+x^5-5x^5ln(x))/(ln(5)x(6+x^5)^2)

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derivative of

\frac{lo g _{5} ( x )}{6 + x ^{5}}

\frac{6 + x ^{5} - 5 x ^{5} ln ( x )}{ln ( 5 ) x ( 6 + x ^{5} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{lo g _{5} ( x )}{6 + x ^{5}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( lo g _{5} ( x ) ) ( 6 + x ^{5} ) - \frac{d}{d x} ( 6 + x ^{5} ) lo g _{5} ( x )}{( 6 + x ^{5} ) ^{2}}

\frac{d}{d x} (lo g_{5} (x)) = \frac{1}{x ln ( 5 )}

\frac{d}{d x} (6 + x^{5}) = 5 x^{4}

= \frac{\frac{1}{x l n ( 5 )} ( 6 + x ^{5} ) - 5 x ^{4} lo g _{5} ( x )}{( 6 + x ^{5} ) ^{2}}

Simplify

\frac{\frac{1}{x l n ( 5 )} ( 6 + x ^{5} ) - 5 x ^{4} lo g _{5} ( x )}{( 6 + x ^{5} ) ^{2}} : \frac{6 + x ^{5} - 5 x ^{5} ln ( x )}{ln ( 5 ) x ( 6 + x ^{5} ) ^{2}}

= \frac{6 + x ^{5} - 5 x ^{5} ln ( x )}{ln ( 5 ) x ( 6 + x ^{5} ) ^{2}}

\frac{\partial}{\partial x} (y cos (y - 2 x))

\int \frac{- y}{y} d y

y^{^{'}} + 2 x (y + 1) = 0

\int_{- 1}^{1} 2 x sin (1 - x^{2}) d x

x^{2 + 6 x}

What is the derivative of (log_{5}(x))/(6+x^5) ?
The derivative of (log_{5}(x))/(6+x^5) is (6+x^5-5x^5ln(x))/(ln(5)x(6+x^5)^2)
What is the first derivative of (log_{5}(x))/(6+x^5) ?
The first derivative of (log_{5}(x))/(6+x^5) is (6+x^5-5x^5ln(x))/(ln(5)x(6+x^5)^2)