What is the derivative of x^{3cos(x}) ?

The derivative of x^{3cos(x}) is 3x^{3cos(x)}(-sin(x)ln(x)+(cos(x))/x)

What is the first derivative of x^{3cos(x}) ?

The first derivative of x^{3cos(x}) is 3x^{3cos(x)}(-sin(x)ln(x)+(cos(x))/x)

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\frac{d}{d x} (x^{3 c o s (x)})

3 x^{3 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Solution steps

\frac{d}{d x} (x^{3 c o s (x)})

Apply exponent rule:

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

x^{3 c o s (x)} = e^{3 c o s (x) l n (x)}

= \frac{d}{d x} (e^{3 c o s (x) l n (x)})

Apply the chain rule:

e^{3 c o s (x) l n (x)} \frac{d}{d x} (3 cos (x) ln (x))

= e^{3 c o s (x) l n (x)} \frac{d}{d x} (3 cos (x) ln (x))

\frac{d}{d x} (3 cos (x) ln (x)) = 3 (- sin (x) ln (x) + \frac{cos ( x )}{x})

= e^{3 c o s (x) l n (x)} \cdot 3 (- sin (x) ln (x) + \frac{cos ( x )}{x})

e^{3 c o s (x) l n (x)} = x^{3 c o s (x)}

= 3 x^{3 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

f (x) = 7 x

\frac{\partial}{\partial x} (x^{2} + 2 x + y^{2})

f (x) = 4 x^{2} - x^{3}

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

What is the derivative of x^{3cos(x}) ?
The derivative of x^{3cos(x}) is 3x^{3cos(x)}(-sin(x)ln(x)+(cos(x))/x)
What is the first derivative of x^{3cos(x}) ?
The first derivative of x^{3cos(x}) is 3x^{3cos(x)}(-sin(x)ln(x)+(cos(x))/x)