What is the derivative of log_{5}(2x^3+x^2) ?

The derivative of log_{5}(2x^3+x^2) is (2(3x+1))/(ln(5)x(2x+1))

What is the first derivative of log_{5}(2x^3+x^2) ?

The first derivative of log_{5}(2x^3+x^2) is (2(3x+1))/(ln(5)x(2x+1))

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\frac{d}{d x} (lo g_{5} (2 x^{3} + x^{2}))

\frac{2 ( 3 x + 1 )}{ln ( 5 ) x ( 2 x + 1 )}

Solution steps

\frac{d}{d x} (lo g_{5} (2 x^{3} + x^{2}))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x^{3} + x^{2}) = 6 x^{2} + 2 x

= \frac{1}{ln ( 5 )} \cdot \frac{1}{2 x ^{3} + x ^{2}} (6 x^{2} + 2 x)

Simplify

\frac{1}{ln ( 5 )} \cdot \frac{1}{2 x ^{3} + x ^{2}} (6 x^{2} + 2 x) : \frac{2 ( 3 x + 1 )}{ln ( 5 ) x ( 2 x + 1 )}

= \frac{2 ( 3 x + 1 )}{ln ( 5 ) x ( 2 x + 1 )}

\int \frac{13}{r ^{2} + 1} d r

e^{x} y \frac{d y}{d x} = e^{- y} + e^{- 8 x - y}

\frac{\partial}{\partial x} ((5 y^{4}) cos (5 x))

f (x) = x + 5, (11, 4)

h (t) = (t + 2)^{\frac{2}{3}} (2 t^{2} - 3)^{3}

What is the derivative of log_{5}(2x^3+x^2) ?
The derivative of log_{5}(2x^3+x^2) is (2(3x+1))/(ln(5)x(2x+1))
What is the first derivative of log_{5}(2x^3+x^2) ?
The first derivative of log_{5}(2x^3+x^2) is (2(3x+1))/(ln(5)x(2x+1))