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Popular >

derivative of x^2sin(3x-2)

Solution

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

Solution

2 x sin (3 x - 2) + cos (3 x - 2) \cdot 3 x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (sin (3 x - 2)) = cos (3 x - 2) \cdot 3

= 2 x sin (3 x - 2) + cos (3 x - 2) \cdot 3 x^{2}

Popular Examples

integral from 0 to 1 of 1/x

\int_{0}^{1} \frac{1}{x} d x

derivative of sec^2(x-tan^2(x))

\frac{d}{d x} (sec^{2} (x) - tan^{2} (x))

limit as t approaches 0 of (5^t-3^t)/t

t \to 0 lim (\frac{5 ^{t} - 3 ^{t}}{t})

f^{^{'}} (a) = 2

(dy)/(dx)=((xe^x)/(ysqrt(9+y^2)))

\frac{d y}{d x} = (\frac{x e ^{x}}{y 9 + y ^{2}})

Frequently Asked Questions (FAQ)

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