Question

y= x^7 - 7x , find dy/dx​

Answer 1

Step-by-step explanation:

y=x

x

+x

7

+7

x

+7

7

Letx

x

=u

Taking log both the sides,

logx

x

=logu

=>xlogx=logu

Differentiating both sides with respect to 'x',

u

1

dx

du

=

x

x

+logx

=>

dx

du

=u×(1+logx)

=>

dx

du

=x

x

×(1+logx)

Now, y=x

x

+x

7

+7

x

+7

7

=>y=u+x

7

+7

x

+7

7

=>

dx

dy

=

dx

du

+7x

6

+7

x

log7+0

=>

dx

dy

=x

x

×(1+logx)+7x

6

+7

x

log7

Answer 2

Answer:

7x⁶-7

Step-by-step explanation:

If y=x⁷-7x, then dy/dx;

dy/dx = d(x⁷-7x)/dx

dy/dx = 7x⁶-7

Note:

• d(x^n) = n*x^n-1