What is the derivative of (x^3+x^2+x+5ln(5x^2-7)) ?

The derivative of (x^3+x^2+x+5ln(5x^2-7)) is (3x^2+2x+1)ln(5x^2-7)+(10x)/(5x^2-7)(x^3+x^2+x+5)

What is the first derivative of (x^3+x^2+x+5ln(5x^2-7)) ?

The first derivative of (x^3+x^2+x+5ln(5x^2-7)) is (3x^2+2x+1)ln(5x^2-7)+(10x)/(5x^2-7)(x^3+x^2+x+5)

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\frac{d}{d x} ((x^{3} + x^{2} + x + 5) ln (5 x^{2} - 7))

(3 x^{2} + 2 x + 1) ln (5 x^{2} - 7) + \frac{10 x}{5 x ^{2} - 7} (x^{3} + x^{2} + x + 5)

Solution steps

\frac{d}{d x} ((x^{3} + x^{2} + x + 5) ln (5 x^{2} - 7))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3} + x^{2} + x + 5, g = ln (5 x^{2} - 7)

= \frac{d}{d x} (x^{3} + x^{2} + x + 5) ln (5 x^{2} - 7) + \frac{d}{d x} (ln (5 x^{2} - 7)) (x^{3} + x^{2} + x + 5)

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

\frac{d}{d x} (ln (5 x^{2} - 7)) = \frac{10 x}{5 x ^{2} - 7}

= (3 x^{2} + 2 x + 1) ln (5 x^{2} - 7) + \frac{10 x}{5 x ^{2} - 7} (x^{3} + x^{2} + x + 5)

\frac{d}{d x} (8 x^{- 2})

\int \frac{x ^{5} - 4 x ^{3}}{x} d x

\frac{( s + 5 )}{( s + 3 ) ( s + 7 )}

f (x) = 2 x - \frac{16}{x}

6 cos (x) + 3 sin^{2} (x)

What is the derivative of (x^3+x^2+x+5ln(5x^2-7)) ?
The derivative of (x^3+x^2+x+5ln(5x^2-7)) is (3x^2+2x+1)ln(5x^2-7)+(10x)/(5x^2-7)(x^3+x^2+x+5)
What is the first derivative of (x^3+x^2+x+5ln(5x^2-7)) ?
The first derivative of (x^3+x^2+x+5ln(5x^2-7)) is (3x^2+2x+1)ln(5x^2-7)+(10x)/(5x^2-7)(x^3+x^2+x+5)