What is the derivative of h(x)=(ln(x))(3x^3) ?

The derivative of h(x)=(ln(x))(3x^3) is 3(x^2+3x^2ln(x))

What is the first derivative of h(x)=(ln(x))(3x^3) ?

The first derivative of h(x)=(ln(x))(3x^3) is 3(x^2+3x^2ln(x))

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derivative of

h (x) = (ln (x)) (3 x^{3})

3 (x^{2} + 3 x^{2} ln (x))

Solution steps

\frac{d}{d x} (ln (x) \cdot 3 x^{3})

Take the constant out:

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

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

Apply the Product Rule:

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

f = ln (x), g = x^{3}

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

\frac{1}{x} x^{3} = x^{2}

= 3 (x^{2} + 3 x^{2} ln (x))

\int e^{4 x + 1} d x

y^{^{''}} + 20 y^{^{'}} + 500 y = 12

\int \frac{1}{cos ^{2} ( x )} d x

x \to 2 lim (\frac{x ^{3} + 7 x + 6}{x ^{3} + x ^{2} - 4 x - 4})

\int \frac{1}{2 ^{2} + 3 x ^{2}} d x

What is the derivative of h(x)=(ln(x))(3x^3) ?
The derivative of h(x)=(ln(x))(3x^3) is 3(x^2+3x^2ln(x))
What is the first derivative of h(x)=(ln(x))(3x^3) ?
The first derivative of h(x)=(ln(x))(3x^3) is 3(x^2+3x^2ln(x))