Solve 1.23507*10^3+5.43219x^10^-1

$$1.23507 \times 10 ^ { 3 } + 5.43219 x ^ { 10 ^ { - 1 } }$$

Evaluate

$$\frac{543219\sqrt[10]{x}}{100000}+1235.07$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$1.23507\times 1000+5.43219x^{10^{-1}}$$

Multiply 1.23507 and 1000 to get 1235.07.

$$1235.07+5.43219x^{10^{-1}}$$

Calculate 10 to the power of -1 and get \frac{1}{10}.

$$1235.07+5.43219x^{\frac{1}{10}}$$

Differentiate w.r.t. x

$$\frac{543219}{1000000x^{0.9}}$$

Steps Using Derivative Rule for Sum

Calculate 10 to the power of 3 and get 1000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1.23507\times 1000+5.43219x^{10^{-1}})$$

Multiply 1.23507 and 1000 to get 1235.07.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1235.07+5.43219x^{10^{-1}})$$

Calculate 10 to the power of -1 and get \frac{1}{10}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1235.07+5.43219x^{\frac{1}{10}})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{10}\times 5.43219x^{\frac{1}{10}-1}$$

Multiply \frac{1}{10} times 5.43219 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{543219}{1000000}x^{\frac{1}{10}-1}$$

Subtract 1 from \frac{1}{10}.

$$\frac{543219}{1000000}x^{-\frac{9}{10}}$$