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Popular >

derivative of f(x)=x^3e^3sin(x)

Solution

derivative of

f (x) = x^{3} e^{3} sin (x)

Solution

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

Solution steps

\frac{d}{d x} (x^{3} e^{3} sin (x))

Take the constant out:

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

= e^{3} \frac{d}{d x} (x^{3} sin (x))

Apply the Product Rule:

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

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

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

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

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

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

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x \to - 2 + lim (x + 11)

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x \to 129 lim (\frac{( x - 129 )}{x + 15 - 12})

inverse oflaplace 5/((s-1)^3)inverse laplace

\frac{5}{( s - 1 ) ^{3}}

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\int x \frac{2}{3} d x

(\partial)/(\partial x)(x^2+xln(yz))

\frac{\partial}{\partial x} (x^{2} + x ln (yz))

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^3e^3sin(x) ?
The derivative of f(x)=x^3e^3sin(x) is e^3(3x^2sin(x)+cos(x)x^3)
What is the first derivative of f(x)=x^3e^3sin(x) ?
The first derivative of f(x)=x^3e^3sin(x) is e^3(3x^2sin(x)+cos(x)x^3)