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

The derivative of (3x^2+ln(x)*(5x^3)^x) is (6x+1/x)(5x^3)^x+(ln(5x^3)+3)(5x^3)^x(3x^2+ln(x))

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

The first derivative of (3x^2+ln(x)*(5x^3)^x) is (6x+1/x)(5x^3)^x+(ln(5x^3)+3)(5x^3)^x(3x^2+ln(x))

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int 7 sin^{5} (x) cos (x) d x

x \to \infty lim (\frac{3 x - 2}{6 x + 1})

\frac{d ^{2} y}{d t ^{2}}

f (x) = arccot (e^{x})

y = x^{2} + x^{- 2} + 7 x - 1

What is the derivative of (3x^2+ln(x)*(5x^3)^x) ?
The derivative of (3x^2+ln(x)*(5x^3)^x) is (6x+1/x)(5x^3)^x+(ln(5x^3)+3)(5x^3)^x(3x^2+ln(x))
What is the first derivative of (3x^2+ln(x)*(5x^3)^x) ?
The first derivative of (3x^2+ln(x)*(5x^3)^x) is (6x+1/x)(5x^3)^x+(ln(5x^3)+3)(5x^3)^x(3x^2+ln(x))