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Popular >

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

Solution

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

Solution

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)

Popular Examples

derivative of ln(1+sqrt(x))

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

sum from n=1 to infinity of (sin(9))^n

n = 1 \sum \infty (sin (9))^{n}

49y^{''}+14y^'+y=0

49 y^{^{''}} + 14 y^{^{'}} + y = 0

derivative of (2x^2+1^{3/2})

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

integral from-2 to 1 of (8x^3-3x^2)

\int_{- 2}^{1} (8 x^{3} - 3 x^{2}) d x

Frequently Asked Questions (FAQ)

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)