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Popular >

derivative of x^xsin(x)

Solution

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

Solution

x^{x} (ln (x) + 1) sin (x) + cos (x) x^{x}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{x}) = x^{x} (ln (x) + 1)

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

= x^{x} (ln (x) + 1) sin (x) + cos (x) x^{x}

Graph

Popular Examples

y(1+x^2)((dy)/(dx))-x(1+y^2)=0

y (1 + x^{2}) (\frac{d y}{d x}) - x (1 + y^{2}) = 0

y^'=-(csc(y))/(sec^2(x))

y^{^{'}} = - \frac{csc ( y )}{sec ^{2} ( x )}

tangent of f(x)=((x-2)/(x+2))^2,\at x=-1 tangent of

f (x) = (\frac{x - 2}{x + 2})^{2}, at x = - 1

integral of 1+cos(x)

\int 1 + cos (x) d x

(cos(x))^{sin(x)}

(cos (x))^{s i n (x)}

Frequently Asked Questions (FAQ)

What is the derivative of x^xsin(x) ?
The derivative of x^xsin(x) is x^x(ln(x)+1)sin(x)+cos(x)x^x
What is the first derivative of x^xsin(x) ?
The first derivative of x^xsin(x) is x^x(ln(x)+1)sin(x)+cos(x)x^x