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Popular >

derivative of (3x^2+6xsin(x))

Solution

\frac{d}{d x} ((3 x^{2} + 6 x) sin (x))

Solution

(6 x + 6) sin (x) + cos (x) (3 x^{2} + 6 x)

Solution steps

\frac{d}{d x} ((3 x^{2} + 6 x) sin (x))

Apply the Product Rule:

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

f = 3 x^{2} + 6 x, g = sin (x)

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

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

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

= (6 x + 6) sin (x) + cos (x) (3 x^{2} + 6 x)

Popular Examples

integral of 9x^2e^{2x}

\int 9 x^{2} e^{2 x} d x

limit as t approaches 0 of I(t)nt

t \to 0 lim (I (t) n t)

integral from 2 to infinity of-2x^{-2}

\int_{2}^{\infty} - 2 x^{- 2} d x

derivative of 2/(sqrt(4x-3))

\frac{d}{d x} (\frac{2}{4 x - 3})

integral of (t^3)/(sqrt(a^4+t^4))

\int \frac{t ^{3}}{a ^{4} + t ^{4}} d t

Frequently Asked Questions (FAQ)

What is the derivative of (3x^2+6xsin(x)) ?
The derivative of (3x^2+6xsin(x)) is (6x+6)sin(x)+cos(x)(3x^2+6x)
What is the first derivative of (3x^2+6xsin(x)) ?
The first derivative of (3x^2+6xsin(x)) is (6x+6)sin(x)+cos(x)(3x^2+6x)