What is the derivative of e^x(xsin(x+(1-x)cos(x))) ?

The derivative of e^x(xsin(x+(1-x)cos(x))) is 2e^xxsin(x)

What is the first derivative of e^x(xsin(x+(1-x)cos(x))) ?

The first derivative of e^x(xsin(x+(1-x)cos(x))) is 2e^xxsin(x)

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\frac{d}{d x} (e^{x} (x sin (x) + (1 - x) cos (x)))

2 e^{x} x sin (x)

Solution steps

\frac{d}{d x} (e^{x} (x sin (x) + (1 - x) cos (x)))

Apply the Product Rule:

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

f = e^{x}, g = x sin (x) + (1 - x) cos (x)

= \frac{d}{d x} (e^{x}) (x sin (x) + (1 - x) cos (x)) + \frac{d}{d x} (x sin (x) + (1 - x) cos (x)) e^{x}

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

\frac{d}{d x} (x sin (x) + (1 - x) cos (x)) = x cos (x) + x sin (x) - cos (x)

= e^{x} (x sin (x) + (1 - x) cos (x)) + (x cos (x) + x sin (x) - cos (x)) e^{x}

Simplify

e^{x} (x sin (x) + (1 - x) cos (x)) + (x cos (x) + x sin (x) - cos (x)) e^{x} : 2 e^{x} x sin (x)

= 2 e^{x} x sin (x)

\int \frac{d m}{m ^{3} + m ^{2}} d x

\frac{d}{d r} (\frac{1}{2 r} + \frac{1}{7 r ^{\frac{6}{7}}})

\int cos (t) sin^{4} (t) d t

\int \frac{x ^{4} + x - 81}{x ^{2} + 9} d x

\frac{\partial}{\partial x} (x z ln (x + 2 y + 3 z))

What is the derivative of e^x(xsin(x+(1-x)cos(x))) ?
The derivative of e^x(xsin(x+(1-x)cos(x))) is 2e^xxsin(x)
What is the first derivative of e^x(xsin(x+(1-x)cos(x))) ?
The first derivative of e^x(xsin(x+(1-x)cos(x))) is 2e^xxsin(x)