What is the derivative of x^{7sin(x}) ?

The derivative of x^{7sin(x}) is 7x^{7sin(x)}(cos(x)ln(x)+(sin(x))/x)

What is the first derivative of x^{7sin(x}) ?

The first derivative of x^{7sin(x}) is 7x^{7sin(x)}(cos(x)ln(x)+(sin(x))/x)

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\frac{d}{d x} (x^{7 s i n (x)})

7 x^{7 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

Solution steps

\frac{d}{d x} (x^{7 s i n (x)})

Apply exponent rule:

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

x^{7 s i n (x)} = e^{7 s i n (x) l n (x)}

= \frac{d}{d x} (e^{7 s i n (x) l n (x)})

Apply the chain rule:

e^{7 s i n (x) l n (x)} \frac{d}{d x} (7 sin (x) ln (x))

= e^{7 s i n (x) l n (x)} \frac{d}{d x} (7 sin (x) ln (x))

\frac{d}{d x} (7 sin (x) ln (x)) = 7 (cos (x) ln (x) + \frac{sin ( x )}{x})

= e^{7 s i n (x) l n (x)} \cdot 7 (cos (x) ln (x) + \frac{sin ( x )}{x})

e^{7 s i n (x) l n (x)} = x^{7 s i n (x)}

= 7 x^{7 s i n (x)} (cos (x) ln (x) + \frac{sin ( x )}{x})

What is the derivative of x^{7sin(x}) ?
The derivative of x^{7sin(x}) is 7x^{7sin(x)}(cos(x)ln(x)+(sin(x))/x)
What is the first derivative of x^{7sin(x}) ?
The first derivative of x^{7sin(x}) is 7x^{7sin(x)}(cos(x)ln(x)+(sin(x))/x)