Solve 0+1/2θ7/8*8*4div9-38-6*965

$$0+ \frac{ 1 }{ 2 } \theta \frac{ 7 }{ 8 \times 8 \times 4 \div 9-38-6 \times 965 }$$

Evaluate

$$-\frac{63\theta }{104392}$$

Solution Steps

Multiply 8 and 8 to get 64.

$$0+\frac{1}{2}\theta \times \frac{7}{\frac{64\times 4}{9}-38-6\times 965}$$

Multiply 64 and 4 to get 256.

$$0+\frac{1}{2}\theta \times \frac{7}{\frac{256}{9}-38-6\times 965}$$

Convert 38 to fraction \frac{342}{9}.

$$0+\frac{1}{2}\theta \times \frac{7}{\frac{256}{9}-\frac{342}{9}-6\times 965}$$

Since \frac{256}{9} and \frac{342}{9} have the same denominator, subtract them by subtracting their numerators.

$$0+\frac{1}{2}\theta \times \frac{7}{\frac{256-342}{9}-6\times 965}$$

Subtract 342 from 256 to get -86.

$$0+\frac{1}{2}\theta \times \frac{7}{-\frac{86}{9}-6\times 965}$$

Multiply 6 and 965 to get 5790.

$$0+\frac{1}{2}\theta \times \frac{7}{-\frac{86}{9}-5790}$$

Convert 5790 to fraction \frac{52110}{9}.

$$0+\frac{1}{2}\theta \times \frac{7}{-\frac{86}{9}-\frac{52110}{9}}$$

Since -\frac{86}{9} and \frac{52110}{9} have the same denominator, subtract them by subtracting their numerators.

$$0+\frac{1}{2}\theta \times \frac{7}{\frac{-86-52110}{9}}$$

Subtract 52110 from -86 to get -52196.

$$0+\frac{1}{2}\theta \times \frac{7}{-\frac{52196}{9}}$$

Divide 7 by -\frac{52196}{9} by multiplying 7 by the reciprocal of -\frac{52196}{9}.

$$0+\frac{1}{2}\theta \times 7\left(-\frac{9}{52196}\right)$$

Express 7\left(-\frac{9}{52196}\right) as a single fraction.

$$0+\frac{1}{2}\theta \times \frac{7\left(-9\right)}{52196}$$

Multiply 7 and -9 to get -63.

$$0+\frac{1}{2}\theta \times \frac{-63}{52196}$$

Fraction \frac{-63}{52196} can be rewritten as -\frac{63}{52196} by extracting the negative sign.

$$0+\frac{1}{2}\theta \left(-\frac{63}{52196}\right)$$

Multiply \frac{1}{2} times -\frac{63}{52196} by multiplying numerator times numerator and denominator times denominator.

$$0+\frac{1\left(-63\right)}{2\times 52196}\theta$$

Do the multiplications in the fraction \frac{1\left(-63\right)}{2\times 52196}.

$$0+\frac{-63}{104392}\theta$$

Fraction \frac{-63}{104392} can be rewritten as -\frac{63}{104392} by extracting the negative sign.

$$0-\frac{63}{104392}\theta$$

Anything plus zero gives itself.

$$-\frac{63}{104392}\theta$$

Differentiate w.r.t. θ

$$-\frac{63}{104392} = -0.0006034945206529235$$

Steps Using Definition of a Derivative

Multiply 8 and 8 to get 64.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \times \frac{7}{\frac{64\times 4}{9}-38-6\times 965})$$

Multiply 64 and 4 to get 256.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \times \frac{7}{\frac{256}{9}-38-6\times 965})$$

Convert 38 to fraction \frac{342}{9}.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \times \frac{7}{\frac{256}{9}-\frac{342}{9}-6\times 965})$$

Since \frac{256}{9} and \frac{342}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \times \frac{7}{\frac{256-342}{9}-6\times 965})$$

Subtract 342 from 256 to get -86.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \times \frac{7}{-\frac{86}{9}-6\times 965})$$

Multiply 6 and 965 to get 5790.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \times \frac{7}{-\frac{86}{9}-5790})$$

Convert 5790 to fraction \frac{52110}{9}.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \times \frac{7}{-\frac{86}{9}-\frac{52110}{9}})$$

Since -\frac{86}{9} and \frac{52110}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \times \frac{7}{\frac{-86-52110}{9}})$$

Subtract 52110 from -86 to get -52196.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \times \frac{7}{-\frac{52196}{9}})$$

Divide 7 by -\frac{52196}{9} by multiplying 7 by the reciprocal of -\frac{52196}{9}.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \times 7\left(-\frac{9}{52196}\right))$$

Express 7\left(-\frac{9}{52196}\right) as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \times \frac{7\left(-9\right)}{52196})$$

Multiply 7 and -9 to get -63.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \times \frac{-63}{52196})$$

Fraction \frac{-63}{52196} can be rewritten as -\frac{63}{52196} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1}{2}\theta \left(-\frac{63}{52196}\right))$$

Multiply \frac{1}{2} times -\frac{63}{52196} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{1\left(-63\right)}{2\times 52196}\theta )$$

Do the multiplications in the fraction \frac{1\left(-63\right)}{2\times 52196}.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0+\frac{-63}{104392}\theta )$$

Fraction \frac{-63}{104392} can be rewritten as -\frac{63}{104392} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(0-\frac{63}{104392}\theta )$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}\theta }(-\frac{63}{104392}\theta )$$

The derivative of ax^{n} is nax^{n-1}.

$$-\frac{63}{104392}\theta ^{1-1}$$

Subtract 1 from 1.

$$-\frac{63}{104392}\theta ^{0}$$

For any term t except 0, t^{0}=1.

$$-\frac{63}{104392}$$