What is the derivative of f(x)=x^2ln(8-5x^2) ?

The derivative of f(x)=x^2ln(8-5x^2) is 2xln(8-5x^2)-(10x^3)/(8-5x^2)

What is the first derivative of f(x)=x^2ln(8-5x^2) ?

The first derivative of f(x)=x^2ln(8-5x^2) is 2xln(8-5x^2)-(10x^3)/(8-5x^2)

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derivative of

f (x) = x^{2} ln (8 - 5 x^{2})

2 x ln (8 - 5 x^{2}) - \frac{10 x ^{3}}{8 - 5 x ^{2}}

Solution steps

\frac{d}{d x} (x^{2} ln (8 - 5 x^{2}))

Apply the Product Rule:

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

f = x^{2}, g = ln (8 - 5 x^{2})

= \frac{d}{d x} (x^{2}) ln (8 - 5 x^{2}) + \frac{d}{d x} (ln (8 - 5 x^{2})) x^{2}

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

\frac{d}{d x} (ln (8 - 5 x^{2})) = - \frac{10 x}{8 - 5 x ^{2}}

= 2 x ln (8 - 5 x^{2}) + (- \frac{10 x}{8 - 5 x ^{2}}) x^{2}

Simplify

2 x ln (8 - 5 x^{2}) + (- \frac{10 x}{8 - 5 x ^{2}}) x^{2} : 2 x ln (8 - 5 x^{2}) - \frac{10 x ^{3}}{8 - 5 x ^{2}}

= 2 x ln (8 - 5 x^{2}) - \frac{10 x ^{3}}{8 - 5 x ^{2}}

y = x^{3} - 10 x, y = 6 x

\frac{d y}{d x} = x^{6} y^{- 5}

\int_{- 5}^{5} \frac{1}{∣ x ∣ ^{\frac{2}{3}}} d x

y = arctan (x)

\frac{\partial}{\partial y} (x^{4} - 2 x^{2} y)

What is the derivative of f(x)=x^2ln(8-5x^2) ?
The derivative of f(x)=x^2ln(8-5x^2) is 2xln(8-5x^2)-(10x^3)/(8-5x^2)
What is the first derivative of f(x)=x^2ln(8-5x^2) ?
The first derivative of f(x)=x^2ln(8-5x^2) is 2xln(8-5x^2)-(10x^3)/(8-5x^2)