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

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

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

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

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\frac{d}{d x} (x^{4 c o s (x)})

4 x^{4 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Solution steps

\frac{d}{d x} (x^{4 c o s (x)})

Apply exponent rule:

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

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

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

Apply the chain rule:

e^{4 c o s (x) l n (x)} \frac{d}{d x} (4 cos (x) ln (x))

= e^{4 c o s (x) l n (x)} \frac{d}{d x} (4 cos (x) ln (x))

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

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

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

= 4 x^{4 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

k = 4 \sum \infty 3 (- \frac{1}{2})^{k}

\int e^{2 x} sin (5 x) d x

y = 55 cos (0.071 x + 0.39) + 63

\int \frac{e ^{3 x} + 2 e ^{x}}{e ^{3 x} + 1} d x

\frac{\partial}{\partial x} (5 y e^{4 x})

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