What is the derivative of 5sin(x(4/(x^3)+3x)) ?

The derivative of 5sin(x(4/(x^3)+3x)) is 5(cos(x)(4/(x^3)+3x)+(-(12)/(x^4)+3)sin(x))

What is the first derivative of 5sin(x(4/(x^3)+3x)) ?

The first derivative of 5sin(x(4/(x^3)+3x)) is 5(cos(x)(4/(x^3)+3x)+(-(12)/(x^4)+3)sin(x))

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\frac{d}{d x} (5 sin (x) (\frac{4}{x ^{3}} + 3 x))

5 (cos (x) (\frac{4}{x ^{3}} + 3 x) + (- \frac{12}{x ^{4}} + 3) sin (x))

Solution steps

\frac{d}{d x} (5 sin (x) (\frac{4}{x ^{3}} + 3 x))

Take the constant out:

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

= 5 \frac{d}{d x} (sin (x) (\frac{4}{x ^{3}} + 3 x))

Apply the Product Rule:

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

f = sin (x), g = \frac{4}{x ^{3}} + 3 x

= 5 (\frac{d}{d x} (sin (x)) (\frac{4}{x ^{3}} + 3 x) + \frac{d}{d x} (\frac{4}{x ^{3}} + 3 x) sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

\frac{d}{d x} (\frac{4}{x ^{3}} + 3 x) = - \frac{12}{x ^{4}} + 3

= 5 (cos (x) (\frac{4}{x ^{3}} + 3 x) + (- \frac{12}{x ^{4}} + 3) sin (x))

What is the derivative of 5sin(x(4/(x^3)+3x)) ?
The derivative of 5sin(x(4/(x^3)+3x)) is 5(cos(x)(4/(x^3)+3x)+(-(12)/(x^4)+3)sin(x))
What is the first derivative of 5sin(x(4/(x^3)+3x)) ?
The first derivative of 5sin(x(4/(x^3)+3x)) is 5(cos(x)(4/(x^3)+3x)+(-(12)/(x^4)+3)sin(x))