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Popular >

derivative of x^2sin(4x-3)

Solution

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

Solution

2 x sin (4 x - 3) + cos (4 x - 3) \cdot 4 x^{2}

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = sin (4 x - 3)

= \frac{d}{d x} (x^{2}) sin (4 x - 3) + \frac{d}{d x} (sin (4 x - 3)) x^{2}

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

\frac{d}{d x} (sin (4 x - 3)) = cos (4 x - 3) \cdot 4

= 2 x sin (4 x - 3) + cos (4 x - 3) \cdot 4 x^{2}

Popular Examples

limit as x approaches-2 of (3x+6)/(x+2)

x \to - 2 lim (\frac{3 x + 6}{x + 2})

integral of (1+e)^5

\int (1 + e)^{5} d x

integral from 1 to 16 of 1/(3-sqrt(x))

\int_{1}^{16} \frac{1}{3 - x} d x

4t*(dy)/(dt)-y=sqrt(t)

4 t \cdot \frac{d y}{d t} - y = t

limit as x approaches 0 of tan(5x)

x \to 0 lim (tan (5 x))

Frequently Asked Questions (FAQ)

What is the derivative of x^2sin(4x-3) ?
The derivative of x^2sin(4x-3) is 2xsin(4x-3)+cos(4x-3)*4x^2
What is the first derivative of x^2sin(4x-3) ?
The first derivative of x^2sin(4x-3) is 2xsin(4x-3)+cos(4x-3)*4x^2