What is the derivative of x^{4sin(x}) ?

The derivative of x^{4sin(x}) is 4x^{4sin(x)}(cos(x)ln(x)+(sin(x))/x)

What is the first derivative of x^{4sin(x}) ?

The first derivative of x^{4sin(x}) is 4x^{4sin(x)}(cos(x)ln(x)+(sin(x))/x)

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\frac{d}{d x} (x^{4 s i n (x)})

4 x^{4 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

Solution steps

\frac{d}{d x} (x^{4 s i n (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{4 s i n (x)} = e^{4 s i n (x) l n (x)}

= \frac{d}{d x} (e^{4 s i n (x) l n (x)})

Apply the chain rule:

e^{4 s i n (x) l n (x)} \frac{d}{d x} (4 sin (x) ln (x))

= e^{4 s i n (x) l n (x)} \frac{d}{d x} (4 sin (x) ln (x))

\frac{d}{d x} (4 sin (x) ln (x)) = 4 (cos (x) ln (x) + \frac{sin ( x )}{x})

= e^{4 s i n (x) l n (x)} \cdot 4 (cos (x) ln (x) + \frac{sin ( x )}{x})

e^{4 s i n (x) l n (x)} = x^{4 s i n (x)}

= 4 x^{4 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

x \to \infty lim (x + 5 x)

y^{^{'''}} + 4 \cdot y^{^{'}} = 3 \cdot x - 1

f (x) = 4 x^{2} + 5 x, at x = - 2

sin (x), x = \frac{π}{3}

y d x + x (ln (x) - ln (y) - 1) d y = 0, y (1) = e

What is the derivative of x^{4sin(x}) ?
The derivative of x^{4sin(x}) is 4x^{4sin(x)}(cos(x)ln(x)+(sin(x))/x)
What is the first derivative of x^{4sin(x}) ?
The first derivative of x^{4sin(x}) is 4x^{4sin(x)}(cos(x)ln(x)+(sin(x))/x)