What is the derivative of sin(x(x^2-27x+6)) ?

The derivative of sin(x(x^2-27x+6)) is cos(x)(x^2-27x+6)+(2x-27)sin(x)

What is the first derivative of sin(x(x^2-27x+6)) ?

The first derivative of sin(x(x^2-27x+6)) is cos(x)(x^2-27x+6)+(2x-27)sin(x)

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\frac{d}{d x} (sin (x) (x^{2} - 27 x + 6))

cos (x) (x^{2} - 27 x + 6) + (2 x - 27) sin (x)

Solution steps

\frac{d}{d x} (sin (x) (x^{2} - 27 x + 6))

Apply the Product Rule:

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

f = sin (x), g = x^{2} - 27 x + 6

= \frac{d}{d x} (sin (x)) (x^{2} - 27 x + 6) + \frac{d}{d x} (x^{2} - 27 x + 6) sin (x)

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

\frac{d}{d x} (x^{2} - 27 x + 6) = 2 x - 27

= cos (x) (x^{2} - 27 x + 6) + (2 x - 27) sin (x)

What is the derivative of sin(x(x^2-27x+6)) ?
The derivative of sin(x(x^2-27x+6)) is cos(x)(x^2-27x+6)+(2x-27)sin(x)
What is the first derivative of sin(x(x^2-27x+6)) ?
The first derivative of sin(x(x^2-27x+6)) is cos(x)(x^2-27x+6)+(2x-27)sin(x)