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Popular >

derivative of 6x^4sin(x)

Solution

\frac{d}{d x} (6 x^{4} sin (x))

Solution

6 (4 x^{3} sin (x) + cos (x) x^{4})

Solution steps

\frac{d}{d x} (6 x^{4} sin (x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (x^{4} sin (x))

Apply the Product Rule:

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

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

= 6 (\frac{d}{d x} (x^{4}) sin (x) + \frac{d}{d x} (sin (x)) x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 6 (4 x^{3} sin (x) + cos (x) x^{4})

Popular Examples

(\partial)/(\partial x)(4x^2-8xy^4+7ay^5-3)

\frac{\partial}{\partial x} (4 x^{2} - 8 x y^{4} + 7 a y^{5} - 3)

taylor sin(x+1)taylor

sin (x + 1)

derivative of-1/2 cot(x)

\frac{d}{d x} (- \frac{1}{2} cot (x))

(dy)/(dx)=e^xy^2

\frac{d y}{d x} = e^{x} y^{2}

derivative of y=(2x+5)/(3x-2)derivative of

y = \frac{2 x + 5}{3 x - 2}

Frequently Asked Questions (FAQ)

What is the derivative of 6x^4sin(x) ?
The derivative of 6x^4sin(x) is 6(4x^3sin(x)+cos(x)x^4)
What is the first derivative of 6x^4sin(x) ?
The first derivative of 6x^4sin(x) is 6(4x^3sin(x)+cos(x)x^4)