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Popular >

derivative of e^xsin(xcos^3(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

integral of ((x^2)/(sqrt(5+2x^3)))

\int (\frac{x ^{2}}{5 + 2 x ^{3}}) d x

limit as x approaches 0 of (5x^n-3x^{n-1}+4x^{n-2})/(2x^n-6x^{n-2)}

x \to 0 lim (\frac{5 x ^{n} - 3 x ^{n - 1} + 4 x ^{n - 2}}{2 x ^{n} - 6 x ^{n - 2}})

derivative of f(x)=5x+3 derivative of

f (x) = 5 x + 3

(\partial)/(\partial x)(-4y^4sin(4x))

\frac{\partial}{\partial x} (- 4 y^{4} sin (4 x))

integral of sin^2(x)cos(3x)

\int sin^{2} (x) cos (3 x) d x

Frequently Asked Questions (FAQ)

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