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)) (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))

f (t) = t^{\frac{5}{3}} e^{t}

\int_{0}^{\infty} e^{- x} cos (x) d x

\frac{\partial}{\partial x} (e^{- 2 t} cos (π x))

\frac{d y}{d t} = \frac{t}{y e ^{y + t^{2}}}

\frac{d}{d x} (sin^{4} (3 x) tan^{3} (4 x))

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))