What is the derivative of x^{5cos(x}) ?

The derivative of x^{5cos(x}) is 5x^{5cos(x)}(-sin(x)ln(x)+(cos(x))/x)

What is the first derivative of x^{5cos(x}) ?

The first derivative of x^{5cos(x}) is 5x^{5cos(x)}(-sin(x)ln(x)+(cos(x))/x)

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\frac{d}{d x} (x^{5 c o s (x)})

5 x^{5 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

Solution steps

\frac{d}{d x} (x^{5 c o s (x)})

Apply exponent rule:

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

x^{5 c o s (x)} = e^{5 c o s (x) l n (x)}

= \frac{d}{d x} (e^{5 c o s (x) l n (x)})

Apply the chain rule:

e^{5 c o s (x) l n (x)} \frac{d}{d x} (5 cos (x) ln (x))

= e^{5 c o s (x) l n (x)} \frac{d}{d x} (5 cos (x) ln (x))

\frac{d}{d x} (5 cos (x) ln (x)) = 5 (- sin (x) ln (x) + \frac{cos ( x )}{x})

= e^{5 c o s (x) l n (x)} \cdot 5 (- sin (x) ln (x) + \frac{cos ( x )}{x})

e^{5 c o s (x) l n (x)} = x^{5 c o s (x)}

= 5 x^{5 c o s (x)} (- sin (x) ln (x) + \frac{cos ( x )}{x})

x \to \frac{π}{4} lim (\frac{tan ( 4 x )}{4 x - π})

\int 3 x^{2} (x^{3} - 5)^{7} d x

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\int_{- 1}^{3} - 2 x^{2} + 4 x + 6 d x

\int \frac{cos ( x )}{1 - cos ^{2} ( x )} d x

What is the derivative of x^{5cos(x}) ?
The derivative of x^{5cos(x}) is 5x^{5cos(x)}(-sin(x)ln(x)+(cos(x))/x)
What is the first derivative of x^{5cos(x}) ?
The first derivative of x^{5cos(x}) is 5x^{5cos(x)}(-sin(x)ln(x)+(cos(x))/x)